An Introduction to Critical Thinking and Creativity: Think More, Think Better

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AN INTRODUCTION TO CRITICAL THINKING AND CREATIVITY

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AN INTRODUCTION TO CRITICAL THINKING AND CREATIVITY Think More, Think Better

Joe Y. F. Lau

® WILEY A JOHN WILEY & SONS, INC., PUBLICATION

Copyright © 2011 by John Wiley & Sons, Inc. All rights reserved Published by John Wiley & Sons, Inc., Hoboken, New Jersey Published simultaneously in Canada No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 750-4470, or on the web at www.copyright.com. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) 748-6011, fax (201) 748-6008, or online at http://www.wiley.com/go/permission. Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives or written sales materials. The advice and strategies contained herein may not be suitable for your situation. You should consult with a professional where appropriate. Neither the publisher nor author shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages. For general information on our other products and services or for technical support, please contact our Customer Care Department within the United States at (800) 762-2974, outside the United States at (317) 572-3993 or fax (317) 572-4002. Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic formats. For more information about Wiley products, visit our web site at www.wiley.com. Library of Congress Cataloging-in-Publication Data: Lau, Joe Y. F., 1968An introduction to critical thinking and creativity : think more, think better / Joe Y.F. Lau. p. cm. Includes bibliographical references and index. ISBN 978-0-470-19509-3 (pbk.) 1. Critical thinking. 2. Creative ability. I. Title. B809.2.L38 2011 153.4'2—dc22 2010048204 Printed in the United States of America. 10 9 8 7 6 5 4 3 2 1

To Amie and Lusina tian xingjian

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CONTENTS

Preface

ix

1

Introduction

1

2

Thinking and writing clearly

11

3

Definitions

21

4

Necessary and sufficient conditions

33

5

Linguistic pitfalls

41

6

Truth

53

7

Basic logic

59

8

Identifying arguments

69 vii

VIII

CONTENTS

9

Valid and sound arguments

75

10

Inductive reasoning

87

11

Argument mapping

95

12

Argument analysis

107

13

Scientific reasoning

113

14

Mill's methods

125

15

Reasoning about causation

133

16

Diagrams of causal processes

141

17

Statistics and probability

145

18

Thinking about values

159

19

Fallacies

173

20

Cognitive biases

185

21

Analogical reasoning

195

22

Making rational decisions

201

23

What is creativity?

215

24

Creative thinking habits

223

Solutions to exercises

233

Bibliography

256

Index

261

PREFACE

This is a textbook on critical and creative thinking. It can be used as a course text or a self-contained study guide. Since there are many similar textbooks in the market, let me describe some special features of this book: • Unlike most textbooks, I discuss both critical and creative thinking because they are equally important for problem solving and they are not independent of each other. We need creativity in critical thinking to come up with arguments, counterexamples, and alternative explanations. And creativity needs critical thinking in evaluating and improving new ideas. They are both part of the essential thinking toolkit. • Good thinking requires not just knowledge of the principles of good reasoning. We discuss them of course, but personality and other psychological factors matter as well. This book emphasizes the importance of attitudes and practice for good thinking. We also discuss findings in cognitive science and psychology, such as cognitive biases in reasoning and decision making. • Our thinking directly affects our life through the choices we make. These choices depend in part on our values and moral outlook. It is of utmost importance that we can think about these issues critically and impartially. I therefore include a chapter on decision making and another one on the foundation of moral reasoning. IX

X

PREFACE

• This book has a companion website: Critical Thinking Web. It is located at http: / /philosophy.hku.hk/think, and hosted by the Philosophy Department of the University of Hong Kong. The website includes many online tutorials that are used in schools and universities around the world. A special section is devoted to this book, which includes errata, additional notes and exercises, and further readings. • This book is not an encyclopedia on thinking skills. It aims to be a short and readable text, providing the reader with a practical and sound foundation. I deliberately leave out a complete treatment of Venn diagrams and standard formal logic. Interested readers and teachers can consult the companion website for online tutorials on these topics. • Useful facts and rules are often presented in bullet points to make them clearer. I also include many examples from finance and business to show how critical thinking is relevant to a variety of careers. A note of warning: To make the text more readable and the sentences shorter, sometimes I simplify and leave out minor qualifications. I am also less strict with the use of quotations marks than I would otherwise be as an academic philosopher. Finally, many of the ideas in the book are not original. They come from other philosophers, psychologists, and experts in other areas. Thanks to Tim van Gelder for his comments on my earlier book proposal. I also want to thank Lee Tien Ming and Jonathan Chan. I have learned a lot about critical thinking from all of them. I would also like to thank Executive Editor Stephen Quigley at John Wiley & Sons, Inc., and Assistant Editor Jacqueline Palmieri. They have been most patient even though I kept missing one deadline after another. On a more technical matter, this book was typeset with ETÈX- It has made the whole project so much more efficient and enjoyable. Thanks to Donald Knuth, Leslie Lamport, and other contributors to the system. Finally, this book is the result of over ten years of teaching in critical thinking. My heartfelt thanks to the many generations of students who endured my classes and smiled politely at my jokes. JoeY.F.Lau Hong Kong January, 2011

CHAPTER 1

INTRODUCTION

1.1

THINKING SKILLS IN THE AGE OF GLOBALIZATION

Whether we like it or not, globalization is changing the way we work and live. First of all, we are increasingly faced with complex problems that affect the whole world, whether it is global warming, pollution, financial crises, or new epidemics. We need good thinking and creative ideas to coordinate efforts to solve these problems. At the personal level, globalization brings about an ever-quickening pace of life. We have a huge amount of information available, but what we learn today might easily become obsolete tomorrow. Although fast changes also bring new opportunities, we now have to compete with talented people across the world. To be successful in this environment, we need good thinking skills that can help us make reliable decisions and acquire new knowledge quickly. But what do we mean by good thinking skills? Basically, it comes down to two things—critical thinking and creativity. Critical thinking is thinking clearly and rationally. It involves thinking precisely and systematically, and following the rules of logic and scientific reasoning, among other things. As for creativity, it is a matter of coming up with new and useful ideas, generating alternative possibilities. This book is about these two sets of thinking skills, but at this point, you might ask, An Introduction to Critical Thinking and Creativity: Think More, Think Better. By Joe Y.E Lau Copyright © 2011 John Wiley & Sons, Inc.

1

2

INTRODUCTION

Which is more important, critical thinking or creativity? The short answer is that they are equally important. We need creativity to come up with ideas to solve problems, but we also need critical thinking to evaluate and improve these ideas. They complement each other, and we need both to survive and to prosper. In this book we shall discuss critical thinking first, and come back to creativity near the end. As we shall see, there is a lot more we can say systematically about critical thinking. A critical thinker is someone who is able to do the following: • Understand the logical connections between ideas. • Formulate ideas succinctly and precisely. • Identify, construct, and evaluate arguments. • Evaluate the pros and cons of a decision. • Evaluate the evidence for and against a hypothesis. • Detect inconsistencies and common mistakes in reasoning. • Analyze problems systematically. • Identify the relevance and importance of ideas. • Justify one's beliefs and values. • Reflect and evaluate one's thinking skills. As we can see from the list, critical thinking skills are essential for all sorts of careers in which we have to communicate ideas, make decisions, analyze, and solve problems. This is why critical thinking is called a domain-general thinking skill. But critical thinking is not just for the workplace. To live a meaningful life and plan for the future, we need to think about ourselves honestly and carefully. The Greek philosopher Socrates (469-399 B.C.E.) once said, "the unexamined life is not worth living." One big difference between human beings and other animals is our capacity for self-reflection. We can examine the purpose and meaning of our life and change ourselves accordingly. Critical thinking contributes to this process of self-evaluation and transformation. Good critical thinking is also the foundation of science and democracy. Science requires rationality in designing experiments and testing theories. A vibrant and progressive democracy requires citizens who can think objectively about social and political issues and are able to avoid biases and prejudices. So obviously the cultivation of critical thinking should be a central aim of education.

1.2

SOME MISCONCEPTIONS ABOUT CRITICAL THINKING

However, critical thinking is sometimes thought to be too confrontational. Some people think critical thinking means criticizing others all the time, which is not constructive. But this is a misunderstanding. Critical thinking is not a purely

IMPROVING OUR THINKING

3

destructive force. First, by rejecting bad ideas, we become better at finding the truth. Second, thinking critically does not mean we criticize people all the time. When other people are right, we don't have to disagree. And when other people are wrong, critical thinking helps us recognize the mistakes being made, but it does not follow we have to publicly denounce them. Sometimes mistakes do not matter. Sometimes we have to be polite, and sometimes we can help people reason better not by criticizing them but by other indirect means—for example, by giving hints and suggestions. A critical thinker can be sympathetic and constructive rather than confrontational. Another objection to critical thinking is that it is not practically useful because people in real life do not listen to reason. They act on the basis of self-interest, emotion, or personal relationships. The first problem with this objection is that it confuses rational thinking with talking about reasons. It might be true that many people are irrational, and to influence them we need to appeal to authority, emotions, or anything other than reason. But we can still use critical thinking to think strategically about the best means to achieve our objectives. The objection is also wrong in assuming that critical thinking is opposed to emotions, relationships, and so on. Consider for example love and friendship. They are certainly valuable, but critical thinking can help us cultivate them. For example, thinking carefully about what is good or bad about a relationship can help us improve it and make it more fulfilling. Besides, it is not always wise to act solely on the basis of emotions. They can be biased by ego, fear, and greed. Thinking more about our decisions can counteract this problem.

1.3

IMPROVING OUR THINKING

So how do we enhance our critical thinking if it is so useful? Obviously, we are all able to think critically to some extent, or we will not survive very long! But there is always room for improvement. Even with a skill as natural as running, training with an expert can improve our breathing and posture and help us run even better. Thinking is something we all do and take for granted, but the fact is that even normally intelligent people can sometimes be stubborn and biased. Psychology research tells us that people make lot of mistakes in their reasoning—they overestimate their abilities, interpret the world to confirm their prejudices, and look for causes and patterns in the wrong places. By studying critical thinking, we are more likely to avoid such errors. We can also help other people by studying critical thinking. Sometimes we get the feeling that an argument is wrong but we do not know exacdy why. Critical thinking gives us the concepts and vocabulary to explain what is wrong. This promotes understanding and more effective discussions. Good critical thinking is a cognitive skill. In general, developing a skill requires three conditions—learning the theory, deliberate practice, and adopting the right attitudes. By theory we mean the rules and facts we have to know in order to possess the skill. For example, one cannot be a good basketball player without

4

INTRODUCTION

knowing the rules of the game—for example, kicking the basketball is not allowed. Likewise, thinking critically requires knowing a certain amount of logic. However, knowing the theory is not the same as being able to apply it. You might know in theory that you should balance the bike when you are cycling, but it does not mean you can actually do it. This is where practice comes in, because it translates your theoretical knowledge into actual ability. However, your attitudes make a big difference as to whether your practice is effective and sustainable. If you hate playing the piano, forcing you to practice is not productive in the long run.

1.3.1 Theory Let us now look at the theoretical knowledge required for good critical thinking. It can be divided into five main areas, and in this book we shall discuss all of them: 1. Meaning analysis: Explain ideas clearly and systematically; use definitions and other tools to clarify meaning and make ideas more precise. 2. Logic: Analyze and evaluate arguments; identify logical consequences and inconsistencies. 3. Scientific methods: Use empirical data to test a theory; identify causes and effects; probability theory and statistics. 4. Decision and values: Rational decision making; critical reflection of value frameworks and moral judgments. 5. Fallacies and biases: Typical mistakes of reasoning and the psychological traits likely to cause such mistakes. Naturally you will find some topics more interesting than others. But whether we are learning martial arts or the piano, there are basic techniques we have to master. They might be boring, but they form the foundation of more advanced techniques. The same is true of critical thinking. Some theories and principles seem rather dry and abstract, but I hope you will appreciate their power and relevance to everyday thinking once you understand how they can be applied.

1.3.2 Practice Psychologists have discovered a 10-year rule when it comes to acquiring a skill. It takes about 10 years of intensive and structured practice—around 10,000 hours of practice—to reach world-class level in a certain area, even for a talented individual. This rule is supposed to apply to all kinds of expertise, whether it is sports, music, chess, writing, or scientific research. Even a genius prodigy such as Mozart spent years practicing musical instruments and writing lesser pieces, under great pressure from his father, who was himself an outstanding musician. Many of Mozart's childhood compositions were arrangements of works by other composers, or they were thought to be partly written by his father. His piano con-

IMPROVING OUR THINKING

5

certo No. 9 (K.271) is perhaps the earliest original work that is highly regarded by critics. But by then Mozart had already been composing for over 10 years. Years of early training and dedicated parents are two typical themes in achieving world-class performance. Tiger Woods has been one of the most successful golf players of all time. His father, Earl, gave him a sawed off a golf club to play with when he was 9 months old. When Tiger was 18 months old, Earl started taking his son to the golf course, and a coach was hired when Tiger was 4 years old. Earl continued to train his son, and just over 10 years later in 1991, Tiger became the youngest ever U.S. Junior Amateur Champion. Of course, it is probably unrealistic to expect all of us to put in the same amount of effort solely into improving our thinking. But what empirical research tells us is that good thinking does not come for free. If we are serious about improving our minds, we have to come up with a plan and be ready to spend a lot of time training. Just reading this book is not going to be enough. You also need to do the exercises and apply your knowledge to your daily life. Critical thinking should become a natural habit, a way of life, rather than something you do occasionally. How do we turn critical thinking into a natural habit? Here is a simple and practical method for you to try out. We call it the fourfold path to good thinking. To follow the method, we make it a habit to ask these four basic questions about the ideas we come across: Question

Issues to think about

What does it mean?

Are the keywords and the main concepts clear? Can the ideas be made more precise? How is it related to other things? Any examples to illustrate what is meant?

How many supporting reasons and objections?

List the reasons for and against the claim. Count and evaluate these reasons. Think about both sides of an issue. Any counterexamples to the claim?

Why is this important or relevant?

What are the major consequences? How does it affect people? Is it useful? Is it surprising? Have I learned something new and interesting?

Which are the other possibilities to consider?

What other information might be relevant? Any similar cases to think about?

These questions look simple, but they are actually quite powerful because they introduce a good structure to organize our analysis. As an example, suppose we are discussing whether it is wrong to eat (nonhuman) animals. Here is how we might apply the fourfold path:

6

INTRODUCTION

1. The first question—what does it mean?—is about clarifying the key concepts so that we can understand more clearly the claim under discussion. • What do we mean by animals'? Dogs and chickens are obviously animals. But what about fish, oysters, insects, bacteria? Is it also wrong to eat them? Where do we draw the line? • If eating animals is wrong, how wrong is it? As bad as killing people? 2. To carry out the second step of the fourfold path, we list all the reasons for and against the claim under consideration. • Arguments against eating meat might include: animals have rights, animal farming create a lot of suffering, and it is more efficient to use land to grow vegetables than to raise animals. • Arguments on the opposite side might include: farm animals exist because of us and so we can do what want with them, and humans are more intelligent than animals. • It is always a good idea to be able to count the number of arguments. For example, three arguments in support and two against. • Think about both sides of an issue. Even if you think eating meat is fine, you should try your best to come up with opposing arguments. You will gain a deeper understanding of your own position and be able to defend it better. • Evaluate the arguments on both sides. What seems to be a good argument might turn out not to be the case on further reflection—for example, why can we eat animals just because we are smarter? Does it also mean adults can eat babies and intelligent aliens can eat human beings? 3. The third step of the fourfold path is to consider whether the issue is important. Does it really matter what the correct answer is? What are the theoretical, social, personal, or political implications? • How would the world be different if more people give up meat? • How important is this question compared with other issues such as poverty and starvation? 4. The last step is to explore alternative possibilities and further issues. • Does the level of intelligence of the animal make a difference? • How about eating animals raised in a happy environment and killed in a painless manner? Is this also wrong? • What about eating animals that die naturally? What if we can grow meat from stem cells and eat meat without killing animals?

IMPROVING OUR THINKING

7

As you can see, although the fourfold path consists of four very simple questions, they help us examine an issue in depth from different perspectives. To improve your thinking, use this method often in your daily life, when you read magazines, surf the web, watch TV, or chat with others. You will become a more sophisticated, systematic, and creative thinker.

Critical thinking and investment The idea that we should think critically might seem downright boring, and yet we should not underestimate the power of critical thinking. It requires having the discipline to reflect on the reasons for our actions, and this is very important if we want to improve ourselves and become more successful. Warren Buffet is one of the world's richest persons, widely admired for his investment record and philanthropy. The adherence to critical thinking is a crucial factor in Buffet's success. Here is what he says about the importance of being able to give reasons for our actions: You ought to be able to explain why you're taking the job you're taking, why you're making the investment you're making, or whatever it may be. And if it can't stand applying pencil to paper, you'd better think it through some more. And if you can't write an intelligent answer to those questions, don't doit. I never buy anything unless I can fill out on a piece of paper my reasons. I may be wrong, but I would know the answer to that. "I'm paying $32 billion today for the Coca-Cola Company because..." If you can't answer that question, you shouldn't buy it. If you can answer that question, and you do it a few times, you'll make a lot of money. Making money might not be our top priority, but if we can apply the same discipline in giving reasons for our actions and think about these reasons carefully, we are more likely to achieve our goals.

1.3.3

Attitude

If you enjoy an activity and believe it is important, you will probably put in more effort and pay more attention to your performance. Similarly, there are positive attitudes that are more conducive to good thinking: • Independence of thought: Good thinking is hard. Some people just want to know the answers rather than work it out themselves. Others have no patience for abstract or complicated ideas. A good thinker is able to think independently and go against conventional wisdom if need be.

8

INTRODUCTION

• Open-mindedness: A good thinker looks at the evidence objectively, and is willing to suspend judgment or change her opinion depending on the evidence. This is not a sign of weakness. An open-minded thinker is not dogmatic. She is willing to admit mistakes, think about new possibilities, and will not reject new ideas without good reasons. • Cool-headedness and impartiality: Good thinking does not require giving up emotions. But we should avoid letting our feelings overwhelm our reasoning. For example, it is difficult to think straight if you get angry easily when other people disagree with you. Fair and objective evaluations help us make better decisions. • An analytical and reflective attitude: Do not jump to conclusions. A good thinker is one who spends time to analyze an issue systematically and carefully and to actively search for arguments and evidence on both sides. She is interested in learning more about her own strengths and weaknesses to improve her performance. These attitudes are crucial for good thinking, but they are more a way of life than a piece of theoretical knowledge. They have to be internalized to become part of our natural habit and personality. This is easier said than done! Good thinking takes a lot of time and effort. But look at it this way: If we are willing to change ourselves when most people don't, this gives us the opportunity to excel and become better than average. EXERCISES Note: Suggested answers are at the end of the book, except questions that are marked with Kl. 1.1 This is a passage from the management best-seller In Search of Excellence (Peters and Waterman, 1982, p. 108). Can you summarize the argument against intelligence and logical thinking? Is it a good argument or not? Explain your reasons. If you place in a botde half a dozen bees and the same number of flies, and lay the bottle horizontally, with its base (the closed end) to the window, you will find that the bees will persist, till they die of exhaustion or hunger, in their endeavor to discover an opening through the glass; while the flies, in less than two minutes, will all have sallied forth through the neck on the opposite side.... It is the bees' love of flight, it is their very intelligence, that is their undoing in this experiment. They evidently imagine that the issue from every prison must be where the light shines clearest; and they act in accordance, and persist in too-logical action. To bees glass is a supernatural mystery. ... And, the greater their intelligence, the more inadmissible, more incomprehensible, will the strange obstacle appear. Whereas

EXERCISES

9

the featherbrained flies, careless of logic ... flutter wildly hither and thither, and meeting here the good fortune that often waits on the simple... necessarily end up by discovering the friendly opening that restores their liberty to them. 1.2

Do you agree with these remarks? Explain your answers. a) Critical thinking is too negative because we are always trying to find fault but this is not a very healthy attitude. b) Critical thinking is not very useful because personal connections and relationships are more important for success. c) We often have to make decisions very quickly without a lot of time to think. So critical thinking is not really that useful.

1.3 Here is another definition of critical thinking from Scriven and Paul (1987). How would you compare this definition with the one in this book? Critical thinking is the intellectually disciplined process of actively and skillfully conceptualizing, applying, analyzing, synthesizing, and/or evaluating information gathered from, or generated by, observation, experience, reflection, reasoning, or communication, as a guide to belief and action. In its exemplary form, it is based on universal intellectual values that transcend subject matter divisions: clarity, accuracy, precision, consistency, relevance, sound evidence, good reasons, depth, breadth, and fairness. 1.4 E3 Apply the fourfold path to the following claims and list the issues and questions you should consider. a) It is always better to have more choices. b) Buying stocks is a good investment because the stock market always goes up in the long run. c) It is not wrong for a person to commit suicide rather than to suffer through a painful terminal illness. 1.5 Here are some questions for you to reflect on your thinking attitudes. Which of them are true of you? a) I can improve my thinking skills further. b) The purpose of thinking is not to be right all the time. c) I am not afraid to try out new ideas. d) Thinking takes time and might not be easy. e) I do not enjoy thinking about complicated ideas. f) Thinking is boring and it is better to spend time doing other things. g) Thinking is easy. I just use my gut feelings to make up my mind. h) The point of giving reasons is to show people that they are wrong.

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CHAPTER 2

THINKING AND WRITING CLEARLY

Do you believe in UFOs? According to a poll in 2005,34% of Americans do. In 2007, Japanese Cabinet Secretary Nobutaka Machimura caused quite a stir when he said on TV that UFOs "definitely" exist. But before you answer the question, pause and think about what UFO means. It is actually an abbreviation for "unidentified flying object." In other words, if there is something in the sky and nobody knows what it is, then it is an UFO. On this interpretation, there are certainly plenty of UFOs, but they could have been weather balloons, atmospheric reflections, and so on. Of course, UFO can also mean an alien spaceship. If this is what is meant, then it is not so clear that there are any. This example shows that when the meaning of a claim is unclear, it might be impossible to say whether it is true or false. Two people might disagree about the existence of UFOs, but the disagreement is pointless if they are using the term to mean different things. Being clear helps us avoid such verbal disputes. The UFO example also illustrates a crucial habit we should cultivate if we want to become a better thinker—before accepting a claim, pause to think about what it means and whether we understand what it says. We are bombarded with sound bites and slogans every day, and we should avoid accepting them uncritically.

An Introduction to Critical Thinking and Creativity: Think More, Think Better. By Joe Y.F. Lau Copyright © 2011 John Wiley & Sons, Inc.

11

12

THINKING AND WRITING CLEARLY

Consider the popular idea that the economy should be a free market without government interference. Before deciding whether we agree or disagree, we need to clarify what a free market is and what counts as interference. For example, surely companies are not free to harm people. But then what about regulating pollution or monopolies? Would investment in education and research count as interference? What about supporting arts and culture or disadvantaged minorities such as the disabled? Once we start thinking about these issues, we begin to realize that a totally free market is undesirable. The real issue is not whether, but how, the government should regulate the economy. Although we should try to improve the clarity and precision of ideas, this is not an absolute rule. Sometimes there is no need to be clear. We do not need to understand the physics of microwave radiation to use a microwave oven. What is important is that we can explain things clearly when we need to. But what kind of skills do we need to be able to think and communicate ideas clearly? We are going to discuss two methods below: enhancing our sensitivity to literal meaning and making connections between ideas.

2.1

LITERAL MEANING

To begin with, we ought to be able to identify the literal meaning of a statement and distinguish it from its conversational implicatures. Literal meaning is a property of linguistic expressions. The literal meaning of a sequence of words is determined by its grammatical properties and the meanings that are conventionally assigned to the individual words. For example, the literal meaning of bachelor in English is "an unmarried man". The phrase I cannot be happier literally means it is impossible for the speaker to be more happy than he or she is right now. On the other hand, the conversational implicature is the information that a speaker implicitly conveys in a particular context, distinct from the literal meaning of what might have been said. Someone who looks at the windows and says, "It is cold here," might be suggesting that the windows be closed. But this message is distinct from the literal meaning of the statement. Similarly, the phrase / love books seems to say that the speaker likes reading, but strictly speaking that is again not part of the literal meaning. The sentence is still true if the speaker does not like to read but loves to collect books as a form of investment or to show off. Of course, good communication skills require sensitivity to conversational implicatures or related clues such as body language. But we should also be able to use literal meaning to convey ideas directly and explicidy. First, it helps us avoid misunderstanding. Second, the truth of what we say generally depends on literal meaning and not the conversational implicature. Suppose I tell you, "I shall try to come to the meeting." This reply is similar to "I will come," but with a significant difference. If I use the first sentence and I fail to show up, I can at least say I tried but could not make it in the end. But if I use the second sentence, I will have made a promise, and failing to show up implies that I have broken my promise and said something false. So if you care about truth and promises, you should care about

CONNECTING IDEAS

13

literal meaning. This is particularly important in law, when it comes to interpreting legislation and contracts. Take the following two clauses for a rental contract. They look similar, but they differ in literal meaning. Which version should you use for your lease if you were a prospective tenant? 1. You may terminate the lease after 12 months by giving 2 months' notice. 2. After 12 months, you may give 2 months' notice and terminate the lease. This example illustrates an important technique in clarifying meaning. One way to explain differences in literal meaning is to identify their different logical implications. The first clause implies a lease that lasts for a minimum of 12 months (if you give notice to leave the apartment at the end of the 10th month), whereas the second one implies a minimum lease of 14 months. Obviously, if you are renting an apartment you want more flexibility and to have the option to move out as early as possible if you need to. So the first clause is preferable. As you can see, attention to literal meaning can clarify our rights and duties and help us avoid unnecessary disputes and nasty surprises later on. Attention to literal meaning is useful in other contexts as well. For example, as consumers we are naturally concerned about the safety and quality of our food, and to make informed choices we need to paying attention to the meaning of food labels. Nowadays lots of foods are supposed to be low-fat, but low-fat does not imply low-sugar or low-salt. Food with "no artificial flavors" can contain preservatives, and "hormone-free" chicken might be injected with lots of antibiotics. Interesting enough, the American food company Tyson at one point was selling chickens advertised as "raised without antibiotics" when in fact the chicken eggs were injected with plenty of antibiotics before they hatched! The company insisted that they had not advertised falsely, because "raised" literally applies only to the bringing up the chicks after they have hatched. Whether you agree with this definition or not, it tells us that those who are concerned about food safety have to be very careful about the meanings of food labels.

2.2

CONNECTING IDEAS

Albert Einstein (1879-1955) once said, "If you can't explain it simply, you don't understand it well enough." Many people are attracted to obscure ideas that they cannot explain. They think the ideas are profound, and they might well be right. But it is often just an illusion. To avoid such self-deception, we should ensure that we can explain our ideas clearly and systematically. The way to do it is to connect our ideas to other ideas. The following sections present some typical methods. 2.2.1

Give examples

Understanding words and concepts through examples is central to learning—think about how children learn words like red and vegetables. Being able to give your

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THINKING AND WRITING CLEARLY

own examples is a good sign that you understand a concept well enough to apply it. Concrete examples are good for illustrating abstract concepts. The speed of light is about 300,000 kilometers per second. This number means nothing to most people. But explain that at this speed you can go round the world seven times in one second, it suddenly becomes very impressive. Choose your examples carefully in your writing and presentations. Vivid and unexpected ones create a deeper impression. Personal stories that your audience can relate to will make your message seem more relevant. Contrasting or opposite examples are also useful, as in explaining why a rule applies in one situation but not another. 2.2.2

Definitions

Definitions can go further than examples in explaining the full meaning of a term. Why are human beings and cows examples of mammals, but fish and turtles are not? You need a definition of mammal to explain why. Definitions are also useful in removing ambiguity and making meaning more precise. (See Chapter 3 for further discussion.) 2.2.3

Identifying implications

To explain theories, proposals, and rules, we can point to their distinctive consequences. In other words, we explain how they make a difference if they are correct or accepted. For example, utilitarianism is the moral theory that the right thing to do in any situation is to choose the action that will maximize the greatest happiness for the greatest number of people. What does that mean? It means we should make more people happy rather than just ourselves. But it also implies that the interests of a small minority can be sacrificed if this will make the majority happier. Similarly, scientists say global warming might lead to a 5°C increase in temperature by 2100. To explain this further, we can list the dire implications, such as rising sea levels, disappearing glaciers, global water shortages, and one third of all species being threatened with extinction. Understanding the consequences of a theory allows us to see its significance and connect it to other ideas. 2.2.4

Compare and contrast

Understanding something implies knowing how it is different from other things. To explain how sentences P and Q are different in meaning, find a situation in which one is true and the other one is false, as in the rental contract example earlier. Similarly, you can explain the differences between concepts by showing that they apply in different situations. Take speed and acceleration. Acceleration is the rate of change of speed. Something moving at a very high speed can in fact have zero acceleration if the speed does not change. Similarly, an object can have a high acceleration if it changes speed very quickly, even if the final speed is very low. In law, there is a difference between charitable and non-profit organizations.

FIVE TIPS FOR EFFECTIVE WRITING AND PRESENTATION

15

All charitable organizations are non-profit, but non-profit organizations need not be charitable. Roughly speaking, charitable ones must be for the benefit of the general public. So a club that aims to benefit only certain private members is not charitable, even if it is not for profit. 2.2.5

Breaking things down

To understand how a complex system works, we can look at its parts and how they interact with each other. A mechanic fixes a car by checking the functions of different parts and see if they fit together properly. A wine buff evaluates a wine by focusing on the different aspects of taste, color, smell, and texture and their balance. Similarly, we can explain an idea more clearly by breaking it down. For example, in this book we explain good thinking in terms of critical and creative thinking. We then define critical thinking as clear and rational thinking, and we can explain clarity and rationality further. A general idea is broken down into smaller concepts, and the smaller concepts are broken down even further, like a tree trunk leading up to the main branches and then smaller and smaller branches. Organizing ideas like a tree has many advantages. It makes them easier to understand and remember. It also helps us adjust the level of details we want to provide in our explanations to other people. We can start with the ideas at the top level, and go down further and further depending on the audience and the time we have. Some people are incapable of explaining anything without launching into a 10-minute speech. But an intelligent person with a deep understanding is just at ease giving a 10-second explanation as a 10-minute one.

2.3

FIVE TIPS FOR EFFECTIVE WRITING AND PRESENTATION

Good communication is not just about using words with the right meaning. We also need to think about how ideas are packaged in a way that is attractive and easy to understand. It would be a pity if you put in a lot of effort but still fail to convey your important ideas. The basic rule is simple enough—make sure that your ideas are simple, organized, and relevant to your readers. It is easier said than done, but improving our writing and presentation can improve our critical thinking as well. Here are five general guidelines. Tip 1 : Know your audience Focus on the points your audience will find interesting and relevant. We can communicate more effectively and leave a better impression. Ask yourself these questions: • How much does the audience know about the topic? Are they professionals or lay people, or both? Provide the appropriate level of information.

16

THINKING AND WRITING CLEARLY

• What do they expect from you? Is your goal to entertain, to inform, or to demonstrate your knowledge? What would the audience be most interested in? Facts, diagrams, predictions, practical advice, or personal stories? • Should you consider any special requirements about the format? Should you provide handouts? Use a projector? Provide a summary? Is there a word or time limit? Tip 2: What is your central message and why is it important? It is an open secret that people who listen to a talk quickly forget most of it. The same goes for students attending lectures. When people remember things, it is because they find something interesting, useful, or funny. So think carefully about the main purpose of your presentation. Is there a take-home message? Focus on it and deliver the message clearly. If everything is important, then nothing will stand out as important. You need to make a choice about which idea to emphasize. If people are going to spend part of their lives listening to you or reading your work, which is the one thing you can point to in order to show that they have not wasted their time? In particular, learn how to formulate a thesis statement for presentation and writing that is analytical in character—that is, involving analyses, arguments, or explanations. The thesis statement is a claim that summarizes the most important point you want to make. Suppose you want to write an essay explaining that people worry too much about radiation from mobile phones. Somewhere near the beginning of the essay you should write down your main point. It sets the tone of the essay and shows the reader what he or she might expect later on. For example, this can be the first sentence of your introduction: Many people believe that mobile phones emit dangerous radiation, but there is to date no convincing evidence that mobile phones cause cancer or other serious health problems. Later on in the essay you can then say more about how worried people might be about this issue and what the relevant scientific studies say. Ideally, your thesis statement should be informative and attract the attention of your reader. (See the companion website for further discussion.) Tip 3: Organize your ideas Good writing takes time to ferment. Always begin with some research and analysis before you start typing out the real thing. Read widely and collect data, diagrams, photos, arguments, articles, and web pages and whatever else might be relevant. When you have collected enough material, think about their connections and the proper order of presentation. Develop the habit of using a point-by-point outline to organize your ideas, where each point might be a concept or a short sentence. The outline helps you distill and organize your ideas.

FIVE TIPS FOR EFFECTIVE WRITING AND PRESENTATION

17

Recently declassified documents in the United States includes a handwritten outline by former President Richard Nixon (1913-1994). Whatever we might think of Nixon,1 his historic visit to China in 1972 was widely regarded as a diplomatic achievement. It was the first time a U.S. president visited the People's Republic of China, and it started the normalization of relations between the two countries. But when he was preparing for his visit, Nixon used the following simple outline to condense the most fundamental issues into a list of bullet points. It might be somewhat surprising to see that complicated diplomatic issues between two countries can be written down on half a page, but the beauty of this outline is that the fundamental issues are organized so clearly:

What they want: 1. Build up their world credentials 2. Taiwan 3. Get US out of Asia What we want: 1. Indochina (?) 2. Communists — to restrain Chinese expansion in Asia 3. In Future — Reduce threat of confrontation by Chinese Super Power What we both want: 1. Reduce danger of confrontation + conflict 2. a more stable Asia 3. a restraint on U.S.S.R

Organization also means being clear about the function of every part of your writing. This includes: • The whole presentation or article should have different parts. An essay typically starts with an introduction, followed by further background information, the supporting evidence and arguments, potential objections, and a conclusion. • Each paragraph should have a clear function—for example, explaining a definition, describing some data, replying to an objection, or adding a qualification. 1 He was involved in the coverup of a politically motivated burglary. The so-called Watergate scandal eventually led to the imprisonment of some of his aides and his own resignation, the first and only resignation of a U.S. president.

18

THINKING AND WRITING CLEARLY

Tip 4: Be simple and direct Leonardo da Vinci (1452-1519) is supposed to have said: "Simplicity is the ultimate sophistication." Many people think profound writing must be difficult and long. So they use complicated sentences and long words to impress people. This is a mistake. Simple writing conveys ideas more clearly. Convoluted writing gives the impression that we are bad at explaining things. In a recent study, people who used plain language were judged to be more clever than those who used long words needlessly (Oppenheimer, 2006). Sometimes people fail to write in a simple way because they want to give as much information as possible. Paradoxically, this can have the opposite effect. People switch off their attention and forget things quickly unless they come across something really interesting. Information overload can therefore bury your main message. So be ruthless and cut out irrelevant material. Go through every word and sentence you have written and see if they can be simplified. Consider this example: If there are any points on which you require explanation or further particulars we shall be glad to furnish such additional details as may be required by telephone. Our telephone number is 555-5555. This sentence is typical of many company brochures, but it is awkward and unnecessarily long. The folllowing is much simpler: For enquiries, please call 555-5555. Some writers are also accustomed to long phrases when in fact simpler ones will do. Here are some common phrases that can be shortened: Phrases in order to in the event that whether or not is in agreement with provide a description of come to the decision

-»

Shorten to to if whether agree with describe decide

Below are some other rules for simple and direct writing. But remember that they are just guidelines with plenty of exceptions. • Break up long sentences (for example, more than 30 words) into shorter ones. Avoid linking sentences with and. • Use the active voice instead of the passive voice. "The customer filed a complaint" rather than "A complaint was filed by the customer."

EXERCISES

19

• Use positive rather than negative terms. "The room was clean" rather than "The room was not dirty." • A good test is to read a passage aloud and see if it sounds clumsy. Easy-toread text has a higher chance of being understood. Tip 5: Rewrite, rewrite, rewrite Good writing does not finish with your first draft. A good author will reread every word and sentence and think about how to make the text even better. Hemingway, who won the Nobel Prize in literature in 1954, said he rewrote the ending to A Farewell to Arms thirty-nine times, just to "get the words right."2 Leonardo da Vinci used a mirror to look at his own painting in reverse so it would look less familiar and he could criticize his work better. This is why it is a good idea to leave your finished writing aside for a while. Read it aloud again later with a fresh eye, and it will be easier to spot problems. Of course, you can also get someone else to read it and give some advice. But try as hard as you can to find something that can be improved, even if it is just deleting a word or changing the order of a few sentences. Good writing is often like a great performance—beautiful to behold and seeming to be without effort, but in reality it is the product of intense labor and love. Rereading what we have written sounds obvious, but it is surprising how few people do it, even when mistakes are costly. A survey of UK recruitment firms found that more than half of the application CVs they have received contain grammatical and spelling errors, leaving a bad impression on prospective employers. Furthermore, applicants aged between 21 and 25 years made the most mistakes. Most firms also said applicants were wasting their time by including details about their hobbies and interests (BBC, 2010). EXERCISES 2.1 For each pair of sentences below, explain whether they differ in literal meaning. a) Do not be evil. Be good. b) I like lobsters. I like eating lobsters. c) We do not add preservatives to our food. Our food contains no preservatives. d) Do not say anything if the police are here. Do not say anything in case the police are here. e) You may kiss the bride. You must kiss the bride. f) Everyone is not sick. Not everyone is sick. He also has this to say about his experience working at a newspaper: "On the Star you were forced to learn to write a simple declarative sentence. This is useful to anyone." He also told F. Scott Fitzgerald, "I write one page of masterpiece to ninety-one pages of shit. ... I try to put the shit in the wastebasket." 2

20

THINKING AND WRITING CLEARLY

g) Nothing that is good is cheap. Nothing that is cheap is good. h) There are many restaurants and the best one is The French Laundry. There is no restaurant better than The French Laundry. 2.2

Kl Howwould you explain the differences in meaning of the following terms? a) eternity, infinity b) ideal, paradigm

2.3 Imagine that following paragraph is taken from a reference letter for a student named Harry. Read each sentence carefully, and explain why the paragraph does not literally say anything positive about Harry. Harry's abilities must be seen to be believed. The amount of material he knows will surprise you. It would be very hard to find someone as capable as he is. He has left a deep impression on all the teachers in the department. You would be fortunate if he works for you. 2.4

How would you rewrite these sentences to make them simpler? a) When the teacher gave the explanation to the class, the explanation was delivered in such a way that it was rather lengthy and could not be easily understood by the students. b) The current situation in this place, which is already tense, turned explosive earlier this month when the international administration, which was put in place after the 1995 peace accord that put an end to the war in Bosnia, gave an order to execute a raid on Herzegovacka Bank. c) In the basement there are four baskets made of bamboo that have got absolutely nothing in them whatever and that might perhaps be given away by us to charitable organizations and societies. d) Anai's used money to purchase a large-type minivan produced by Toyota that is red in color. e) Apple has designed a laptop that is quite special—the case of the laptop is made from the material aluminum and is not composed of any smaller parts.

2.5 M Take something you have written a few years ago, and read it again to see how it can be improved in light of the suggestions here.

CHAPTER 3

DEFINITIONS

Definitions are very useful in explaining and clarifying meaning. A typical definition has two parts: • The definiendum: the term being defined ^ bachelor = unmarrie man d

// • The definiens: the words that define the definiendum-^ People often use is instead of the equality sign in giving definitions—for example, a bachelor is an unmarried man. A bit more terminology: • A term is a referring expression in a language made up of one or more words, such as The United Nations, Beethoven, mammals, purple. An Introduction to Critical Thinking and Creativity: Think More, Think Better. By Joe Y.F. Lau Copyright © 2011 John Wiley & Sons, Inc.

21

22

DEFINITIONS

• The referent of a term is what the term refers to. So the terms listed in the last paragraph refer respectively to an organization, a person, a class of animals, and a particular shade of color. A term such as Mount Everestrefers to a real physical thing in the world, but other terms such as truth and 13467 refer to more abstract things. The set of things a term refers to is known as the extension of the term. So dolphins, humans, donkeys, gorillas are all within the extension of mammals. • The concept associated with a term is an idea that encapsulates our understanding of the term. Although a term is made up of words, a concept is not. Agua is a Spanish word distinct from the English word water. They have different spelling and pronunciation, but they have the same meaning and express the same concept. In this book we shall take definitions to be primarily definitions of terms, although we can loosely speak of defining a concept (that is, defining the term that expresses the concept). We can divide definitions into three kinds according to their purpose: stipulative, reportive, and precising.

A definition worth US$7 billion On September 11,2001, terrorists destroyed the twin towers of the World Trade Center in New York City by crashing two planes into them. At the time, Larry Silverstein was holding a 99-year lease for the buildings. The buildings were covered by insurance which would pay US$3.55 billion for an "occurrence" of a terrorist attack. But Silverstein argued that he should get double the amount, because there were two occurrences of attacks, as there were two planes that hit the buildings about 15 minutes apart. Obviously, the insurers claimed this was just one occurrence of a coordinated attack. So here is a definition that is worth a few billion dollars! This is a good example about the importance of definitions in contracts and official documents. (The trial was a long and complicated affair. In the end a jury decided that there were two occurrences, even though Silverstein did not get the full amount he wanted.)

3.1

REPORTIVE DEFINITION

A reportive definition is also known as a lexical definition. It reports the existing meaning of a term. Here are some examples: • Prime number = any integer greater than 1 and divisible only by 1 and itself. • WTO stands for "The World Trade Organization".

REPORTIVE DEFINITION

23

• Sushi is a kind of food made with vinegared rice with some meat or vegetable topping. Obviously, reportive definitions are useful for learning new words in a language. The main criterion for evaluating a reportive definition is that the meaning of the definiens should match the meaning of the definiendum exactly. This means the definition should not be inconsistent with the existing usage of the term in question. Suppose someone consults a very old dictionary that defines computer as "a person whose job is to carry out mathematical calculations." This definition was before modern electronic computers were invented. It is inconsistent with how we actually use the word computer today, and so it is no longer a good reportive definition. A correct reportive definition should not be too wide or too narrow. A definition is too wide if the definiens applies to things that the definiendum does not apply to. In other words, the definition includes things that it should not. For example, defining an airplane as a flying machine is too wide, since helicopters are also flying machines but they are not airplanes. The situation is indicated by the Venn diagram below. The thick circle represents the set of all airplanes, and the bigger circle represents all flying machines. Since all airplanes are flying machines, the thicker circle is inside the other one. But there are plenty of flying machines within the larger circle that are not airplanes, such as helicopters, rockets, and airships.

helicopter -jetfighter flying machines A definition is too narrow if the definiens fails to include things to which the definiendum applies. In other words, the definition fails to include things that it should. Consider the definition of religion as any belief system that includes worshiping a god who created the universe. This definition is too narrow since it excludes religions that do not postulate a creator, such as Jainism and certain versions of Buddhism and Daoism.

Daoism -^. f ^ ^ I religions X ^

/-—-s"\ f \ \ ^ ^ _ ^ belief systems that \^ * N < | worship a creator ^S

Christianity

Notice that a definition can be too wide and too narrow at the same time. Suppose someone defines bravery as "not running away from danger". The definition

24

DEFINITIONS

is too wide because even a coward might fail to run away from danger. Perhaps he is immobilized by fear, or perhaps he does not even realize that he is in danger. But the definition is also too narrow because a person can be brave even if he avoids dangerous situations. Bravery does not require stupidity. There is no reason why a fireman who escapes from a burning building cannot be brave. c j escaping from danger without panicking

*■ ~

bravery "

3.2

/-x. ^

^

\

'

/ frozen with fear ^ not running away from danger

STIPULATIVE DEFINITION

A stipulative definition is used to assign a new meaning to a term, whether or not the term has an existing meaning. If the stipulative definition is accepted, then the term is used in the new way that is prescribed. Suppose we agree to define IBM to mean "incredibly boring movie". Once this is accepted, we can then say things like "Cable TV is showing another IBM right now." Stipulative definitions are not just for secret codes and acronyms. They are also used to introduce new technical terms—for example, quark (physics), priori (biology), risk premium (economics). Notice that a stipulative definition does not have to be faithful to the old meaning of the term being defined, if it has any. In physics, a strange quark is just one type of elementary particle, and it is not particularly strange. In a stipulative definition, the meaning of the definiendum is completely determined by the meaning of the definiens, whatever it is, so the question of whether it is too wide or too narrow simply does not apply. One more point to bear in mind about stipulative definitions: If you define a term more than once, make sure that the definitions are equivalent. Otherwise confusion might arise due to the inconsistent definitions. 3.3

PRECISING DEFINITION

A precising dennition is something in between reportive and stipulative definitions. The function of a precising definition is to make the meaning of a term more precise. Suppose a bus company wants to give discounts to old people. If the company simply declares, "old people pay only 50% of the full fare," this would be too vague because it is not clear when a person becomes old. Some people might say that being 60 is old, but others might disagree. To avoid disputes and uncertainty, the company might define old person to mean "any person of age 65 or older." This definition is in part stipulative because there is no special reason why age 65 should be chosen as the cut-off point, as opposed to say 64 or 66. But

PRECISING DEFINITION

25

it is not entirely arbitrary because given the purpose of the definition, it would be inappropriate to adopt a definition that classifies children as "old." As we can see, one major function of precising definitions is to make laws and regulations more precise, so there is less uncertainty regarding their application. Precising definition are also useful in resolving verbal disputes. A verbal dispute is a disagreement that is due solely to the ambiguity of a term. The American philosopher William James (1842-1910) once told this story about some hunters in a forest. One of the hunters was standing on one side of a tree and there was a squirrel climbing on the other side of the tree trunk. The hunter tried to look at the squirrel by walking around the tree, but the squirrel kept moving around the tree as well and always stayed on the opposite side of the tree trunk. Now the hunter certainly circled the tree, and the squirrel was on the tree. But did the hunter go round the squirrel or not7. The hunters entered into a heated debate about this, and it was left to James to adjudicate. He explained that it all depends on what go round means: If you mean passing from the north of him to the east, then to the south, then to the west, and then to the north of him again, obviously the man does go round him, for he occupies these successive positions. But if on the contrary you mean being first in front of him, then on the right of him, then behind him, then on his left, and finally in front again, it is quite as obvious that the man fails to go round him, for by the compensating movements the squirrel makes, he keeps his belly turned towards the man all the time, and his back turned away. Make the distinction, and there is no occasion for any farther dispute. (James, 1995, p. 17) This is a dispute that a precising definition can resolve. The ordinary meaning of go round is not precise, and a more fine-grained distinction accurately pinpoints the source of disagreement. Verbal disputes are contrasted with factual disputes, which are disagreements about facts rather than meaning. If someone thinks Sydney is the capital of Australia and others disagree, then this is a factual dispute that can be resolved by checking the facts. Many disputes are a mixture of verbal and factual disputes, and we should separate them out to advance the discussion. Often, the first step is to use precising definitions to clarify the issue. Take the question of whether nonhuman animals have language. To answer this question, we should be more precise about what language means. If it refers to any system of communication, then obviously birds and other animals have languages, since they do communicate with each other. On the other hand, language might also be used in a different sense, requiring the use of words to form sentences according to a system of grammar or being able to communicate about arbitrary objects and situations, including those that might be far away and distant in time. Given this definition, many animal communication systems do not qualify as languages. It is of course possible that some mammals such as chimpanzees might possess language in this more

26

DEFINITIONS

sophisticated sense. Precising definitions allow us to refine questions, so we can gain a better understanding of how to answer them. 3.4

CRITERIA FOR GOOD DEFINITIONS

We have said that a reportive definition should not be too wide or too narrow. Here are more criteria for evaluating all kinds of definitions, not just reportive ones. 3.4.1

Use intensional definitions if possible

Philosophers very often draw a distinction between the extension and intension of a term (or concept). The extension of a term is the set of things to which the term applies. So for example, the extension of prime number is set of numbers {2, 3, 5, 7, 11, 13,...}. On the other hand, the intension of a term is its meaning. The intension of prime number would be "any integer larger than one which is completely divisible only by one and itself." When we define a term, should we define it by extension or intension? It depends, but we should use intensional definition where possible. A term such as human beinghas a very large extension. It is impossible to define the term by listing all the human beings there are. Furthermore, even if we are able to list all the items in the extension of a term, this might not explain the criterion for including them. Defining prime numbers as 2, 3, 5, 7, 11, ... fails to explain how the numbers are selected and how the list should continue. An intensional definition is better. However, in some situations, an intensional definition might not be available. The seven deadly sins, for example, is understood as referring to pride, greed, envy, anger, lust, gluttony, and sloth. There is of course a long story about the history of the term and why it is these seven sins that appear on the list. However, this history is not relevant to the definition of the list. 3.4.2

Avoid circularity

A good definition should avoid circularity. A circular definition is one where the definiens cannot be understood without knowing the meaning of the definiendum. Consider the definition of time as "a quantity measured by clocks or watches." This definition is circular because we cannot fully explain what clocks and watches are without taking them as instruments that measure time. Similarly, sometimes people say "the meaning of life is to search for the meaning of life." This sounds profound, but taken as a definition, it is hopelessly circular and does not make much sense. If the meaning of life is to search for the meaning of life, then it follows that the meaning of life is to search for a search for the meaning of life, which is to search for a search for a search of the meaning of life, and so on. Of course, on a more charitable interpretation, perhaps the suggestion is that the mere process of searching for the meaning of life is itself sufficient to make one's life meaningful. But this does not seem very plausible. Imagine a selfish and bitter person who

DEFINITION TECHNIQUES

27

contributes nothing to the world, who spends his entire life doing nothing except being obsessed with the question of what the meaning of life is. This does not seem like a very meaningful life at all. 3.4.3

Avoid obscurity

Definitions should avoid obscure and metaphorical language as far as possible. "Science is searching for a black cat in a dark room" might convey an amusing image of the difficulty of scientific research, but as a definition it is too obscure to tell us much about the nature of science. However, a reportive definition should not be more precise than the term that is being defined. A ship might be defined as a vessel of considerable size for navigating on water. This definition is vague because it is unclear what considerable size means. But this is in itself not a good objection to the definition, because our concept of a ship is vague in exactly the same way. Defining a ship as a vessel longer than 30 meters will make the definition too precise and end up distorting the ordinary meaning of the word. 3.4.4

Avoid persuasive definitions

Finally, definitions should also avoid inappropriate emotional connotations. A persuasive definition is a definition that attaches a positive or negative emotional meaning to a term when there is in fact no such association. For example, if someone defines democracy as "dictatorship by the poor and the uneducated," obviously such a person does not think very highly of democracy. But whether democracy is a good or bad thing should depend on further arguments and not be decided solely by a definition. Similarly, consider the definition "abortion is the termination of pregnancy by murdering an unborn child." This definition assumes that abortion is wrong because it classifies abortion as murder. But it is surely possible to understand abortion in a more neutral way. The biased definition that is proposed distorts the ordinary meaning of the term. (Another problem with the definition is that it assumes without argument that the aborted fetus is already a child—that is, a person.) This is not to deny that a persuasive definition can be a useful rhetorical tool. They are often used in debates and political speeches, but we should avoid them in a rational and fair-minded discussion. 3.5

DEFINITION TECHNIQUES

Here are some of the different ways of formulating a definition. 3.5.1

Definition by synonym

In a definition by synonym, a word (or a short term) is defined by giving another term that has exactly the same meaning—for example, physicians = doctors, lawyer = attorney, ameliorate = improve, and prognosticate = predict.

28

DEFINITIONS

3.5.2

Definition by ostension

An ostensive definition explains the meaning of a term by giving examples, as when we explain the meaning of red to children by pointing to examples of red things. Or someone might explain a professional as "people like doctors, lawyers, and accountants." Ostensive definitions are useful when it is difficult to explain the meaning of a term precisely. But an ostensive definition is a form of definition by extension, and intensional definitions can explain meaning better if they are available. 3.5.3

Definition by genus-differentia

The genus-differentia method is a very useful tool for constructing definitions. According to this approach, when we want to define a term, first we identify the broad category that the term is supposed to apply to. This category is known as genus. To define mule, we note first of all that a mule is an animal. Of course, there are many kinds of animals other than mules. So the next step is to identify the differentia. This is the property that separates the items in the genus into two groups—those that fall within the extension of the definiendum, and those that do not. In the case of mule, this would be the property of being the offspring of a male donkey and a female horse. Putting the two parts together, we arrive at the full definition: • A mule is an animal that is the offspring of a male donkey and a female horse. This type of definition is useful because it informs the audience about the kind of thing the definiendum applies to, even if the complete definition is difficult to remember and understand. Here are more examples of this kind of definition, with the genus part underlined: • Ice = frozen water. • Witness = a person who testifies under oath at a trial or deposition. • Vitamin = a low molecular weight organic compound required in trace amounts for normal growth and metabolic processes. • Bear market = a prolonged condition of the financial market in which investment prices fall and accompanied by widespread pessimism. • Phoneme = the smallest unit of sound in a language. 3.6

THREE MISCONCEPTIONS ABOUT DEFINITIONS

Definitions are no doubt useful, and this has led some people to claim that we should define all the words we use. But this is far too extreme. First of all, we do

EXERCISES

29

not have to be precise and clear all the time. Otherwise we have to throw away lots of jokes, poems, and ordinary conversations. Also, many words are difficult to define. We learn words like green, warm and cold through examples and not complete definitions. Other words like time and existence seem so basic and hard to define even though we understand them well enough in everyday life. In any case, it is surely impossible to define all the words we use without circularity, since our language contains only a finite number of words. A second misconception about definitions is to think that dictionaries provide the most accurate and authoritative definitions. Dictionaries are of course useful in learning a language, but dictionary entries often describe only the main usage of a term, leaving out its more subtle aspects. An entry might also include extra factual information that is not part of the meaning of the term. According to The Pocket Oxford Dictionary of Current English, a cat is a small soft-furred four-legged domesticated animal. As a definition it is both too wide and too narrow, because a small furry dog is not a cat, and a cat that has become large as a result of hormonal injection does not thereby cease to be a cat. Another point to remember is that a lot of terms have technical meanings, such as inflation in economics and mass in physics. A general dictionary might not give you the correct explanation. You need to consult a more specialized dictionary for that particular discipline. Finally, the definitions of many abstract concepts can be controversial. Think of art, justice, knowledge, rationality. A short dictionary entry might be a good start to help us think more deeply about these concepts, but we should not expect a dictionary to give us the final word on their proper understanding. A third misconception about definition is the belief that to know the real meaning of a term, we have to find its original definition or meaning. Many people like to explain X by beginning with the history of the word X. The etymological fallacy is the mistaken idea that we always need to look at the history and original usage of a term to decide what its current meaning is. For instance, the word passion derives from a Latin root that means "suffering." But it would be a bad argument to judge that a certain relationship is not really passionate because the parties involved are not suffering. The current meaning of a word depends on how it is actually used, and there is no reason why meaning and usage cannot change drastically over a long period of time. EXERCISES 3.1

Classify these definitions as reportive, precising, stipulative or persuasive: a) Above average intelligence means "having an IQ of more than 100." b) A camera is an instrument for taking photos. c) Animal rights activists are people who love animals more than human beings. d) An atheist is a person who does not believe in the existence of God. e) X is harder than Y = X can make a scratch on Y but not the other way round.

30

DEFINITIONS

3.2

Evaluate these definitions and see if they have any problems. a) Hatred = the wish to harm other people or to ruin something that is important to them. b) Biology is when you study living organisms. c) What is Yin? Not Yang. What is Yang? Not Yin. d) Love is the master key that opens the gates of happiness. (Oliver Wendell Holmes) e) Love is the affinity experienced between two people who are naturally able and willing to tune into one another's emotional, intellectual, and physical states—and respond to them in a nurturing and a stimulating way. (biomatch.com) f) Furious = being angry at someone. g) A bomb is a device designed to explode so as to hurt people.

3.3

E3 How would you define vegetable! a) What do you think of the definition of vegetable as an edible plant or part of an edible plant that is not a seed or a sweet fruit? b) Would the following items count as vegetables under this definition: rice, avocado, mushroom, ginko nut, peanut, lemon, lotus seed, tomato juice?

3.4

What is wrong with these arguments, if anything? a) Philosophy originally meant "love of wisdom" in Greek. If you are a philosopher, you must be very wise. b) Art originally meant "to make." So art is created whenever someone makes something.

3.5 Insider trading is a crime in most countries. Suppose you are a legislator trying to draft regulation prohibiting insider trading. How would you define it? What about this definition: Insider trading is any sale or purchase of the shares or bonds of a company that relies on information about the internal operations of the company. 3.6

Consider this definition of domestic violence from a 2004 UK crime survey: Any violence between current or former partners in an intimate relationship, wherever and whenever the violence occurs. The violence may include physical, sexual, emotional or financial abuse. a) Is it possible to simply it further? Which is the most important part? b) Compare the survey definition with the following one from a women's self-help group. Identify the main differences and their respective strengths and weaknesses: Domestic violence is physical, psychological, sexual or financial violence that takes place within an intimate or family-type relationship and forms a pattern of coercive and controlling behavior.

EXERCISES

3.7

31

Evaluate these definitions. Come up with as many objections as you can. a) Sexual harassment is any action related to sex that makes someone distressed or unhappy. b) Harassment means being told that a raise, promotion, or other benefit is dependent on you going on a date with your boss or some other similar activity.

3.8 A lawyer suggests defining the word container as "a receptacle having at least one exterior surface and a plurality of walls defining a discrete object receiving volume." What is your opinion? 3.9 K Give definitions of these terms using the genus-differentia method: orphan, portrait, ballpoint pen, square, even number.

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CHAPTER 4

NECESSARY AND SUFFICIENT CONDITIONS

Necessary and sufficient conditions help us understand and explain the connections between concepts, and how different situations are related to each other.

4.1

NECESSARY CONDITIONS

To say that X is a necessary condition for Y is to say that the occurrence of X is required for the occurrence of Y (sometimes also called an essential condition). In other words, if there is no X, Y would not exist. Examples: • Having four sides is necessary for being a square. • Infection by HIV is necessary for developing AIDS. • Having die intention to kill someone or to cause grievous bodily harm is necessary for murder. To show that X is not a necessary condition for Y, we simply find a situation where Y is present but X is not. Examples: An Introduction to Critical Thinking and Creativity: Think More, Think Better. By Joe Y.F. Lau Copyright © 2011 John Wiley & Sons, Inc.

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• Eating meat is not necessary for living a healthy life. There are plenty of healthy vegetarians. • Being a land animal is not necessary for being a mammal. Whales are mammals, but they live in the sea. In daily life, we often talk about necessary conditions, maybe not explicitly. When we say combustion requires oxygen, this is equivalent to saying that the presence of oxygen is a necessary condition for combustion. Note that a single situation can have more than one necessary condition. To be a good pianist, it is necessary to have good finger technique. But this is not enough. Another necessary condition is being good at interpreting piano pieces. 4.2

SUFFICIENT CONDITIONS

If X is a sufficient condition for Y, this means the occurrence of X guarantees the occurrence of Y. In other words, it is impossible to have X without Y. If X is present, then Y must also be present. Some examples: • Being a square is sufficient for having four sides. • Being a grandfather is sufficient for being a father. To show that X is not sufficient for Y, we list cases where X occurs but not Y: • Being infected by HIV is not sufficient for developing AIDS because there are many people who have the virus but have not developed AIDS. • Loyalty is not sufficient for honesty because one might have to act in a dishonest manner to protect the person one is loyal to. Note that a single state of affairs can have more than one sufficient condition. Being red and being green are different conditions, but they are both sufficient for something being colored. 4.3

DESCRIBING HOW TWO THINGS ARE CONNECTED

Given any two conditions X and Y, there are four ways in which they might be related to each other: 1. X is both (jointly) necessary and sufficient for Y. 2. X is necessary but not sufficient for Y. 3. X is sufficient but not necessary for Y. 4. X is neither necessary nor sufficient for Y.

THE WRITE-OFF FALLACY

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Some examples: 1. Being an unmarried man is necessary and sufficient for being a bachelor. 2. Oxygen is necessary but not sufficient for our survival. 3. Having a son is sufficient but not necessary for being a parent. 4. Being rich is neither necessary nor sufficient for a happy life. This fourfold classification is useful because it provides the starting point for analyzing how things are related. When we think about the relationship between two things X and Y, we can begin by asking whether one is necessary or sufficient for the other. For example, what is the connection between democracy and the rule of law? First, we might say that the rule of law is necessary for democracy. A democracy is impossible if people do not follow legal procedures to elect leaders or resolve disputes. But we might also add that the rule of law is not sufficient for democracy, because the legal rules that people follow might not be fair or democratic. As this example shows, the concepts of necessary and sufficient conditions can be very useful in studying and teaching. When you understand a subject more deeply, you do not just memorize individual pieces of information. You should also be able to understand the connections between the basic concepts, and this includes relationships of necessity and sufficiency. Necessary and sufficient conditions are also related to the topic of definition. In effect, a definition of X provides conditions that are both necessary and sufficient for X. When we define a bachelor as an married man, this implies that being an unmarried man is both necessary and sufficient for being a bachelor. 4.3.1

Using necessary and sufficient conditions to resolve disputes

The concepts of necessary and sufficient conditions are quite simple, but they are very useful and fundamental concepts. Sometimes when people disagree with each other, especially about some theoretical issue, we can use these concepts to identify more clearly the differences between the parties. For example, suppose someone claims that computers cannot think because they can never fall in love or be sad. To understand this argument better, we can ask whether this person is assuming that having emotions is necessary for thinking, and if so why? If something is capable of reasoning and deduction, then presumably it can think. But emotions seem to be a different category of mental states. We can imagine a person who is able to think and reason, but who cannot feel any emotion, perhaps due to brain injuries. If this is possible, it shows that emotions are not necessary for thinking. 4.4

THE WRITE-OFF FALLACY

Although the concepts of necessary and sufficient conditions are very important, they are also used in some bad arguments. One such fallacy, which we might call

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NECESSARY AND SUFFICIENT CONDITIONS

the write-off fallacy, is to argue that something is not important, because it is not necessary or not sufficient for something else that is good or valuable. For example, some people argue that democracy is not really that important because it is not necessary for having a good government. It is possible for a nondemocratic government to work efficiently for the interests of the people, and this might be correct. Furthermore, democracy is not sufficient for good governance either, since citizens can make bad choices and end up electing a bad government. This is also possible. However, it might still be the case that a democratic political system is more likely to produce a good government than other alternatives.1 In principle, a benevolent dictator can be a wise and competent ruler, but the fact is that this is extremely rare, and dictators are more likely to abuse their power. The general lesson here is that a condition C can be an important factor that makes an effect E more likely to happen, even if C is neither necessary nor sufficient for E. It is not enough to write off C as unimportant simply by pointing to isolated cases where there is C but no E, or where there is E but no C.

4.5

DIFFERENT KINDS OF POSSIBILITY

Necessary and sufficient conditions are related to the concept of possibility. To say that X is necessary for Y is to say that it is not possible for Y to occur without X. To say that X is sufficient for Y is to say that it is not possible for X to occur without Y. There are, however, different senses of possibility, and corresponding to these different sense there are different kinds of necessary and sufficient conditions. Let us consider these statements: • It is impossible to draw a red square without drawing a square. • It is impossible to dissolve gold in pure water. • It is impossible to travel from India to France in less than one hour. • It is impossible to vote in Australia if you are under 18. The word impossible does not have the same meaning in these statements. In the first statement, what is being referred to is logical impossibility. Something is logically impossible if it is contradictory or against the laws of logic. Thus a round square is a logical impossibility, and it is logically impossible for there to be a red square without there being a square. But it is not logically impossible to dissolve gold in water. Logic itself does not tell us that this cannot happen. Rather, the impossibility is due to the laws of physics and chemistry that happen to hold in our universe. If our universe had 'Here is a famous quote from Winston Churchill (1874-1965): "No one pretends that democracy is perfect or all-wise. Indeed it has been said that democracy is the worst form of government except all those other forms that have been tried from time to time." (Speech in the House on the Parliament Bill, Novemberll, 1947)

EXCLUSIVE AND EXHAUSTIVE POSSIBILITIES

37

operated differently, then perhaps gold would dissolve in water. Dissolving gold in water is therefore logically possible but empirically impossible. Empirical possibility is sometimes also known as causal or nomological possibility. The sense in which the third statement is true is again different. The laws of physics probably do not stop us from traveling from India to France within an hour. Perhaps such a short trip is possible with some future airplane, but it is certainly not possible at this point in time. When current technology does not permit a situation to happen, we say that it is technologically impossible, even though it might be both logically and empirically possible. Of course, what is currently technologically impossible might well turn out to be technologically possible in the future. Finally, voting under the age of 18 is certainly not prohibited by logic, the laws of nature, or current technology. What is meant by impossible in the fourth statement is thus something else—namely legal impossibility. To say that X is not possible in this sense is to say that X is incompatible with the relevant legislation. Note that what we have just said about the different senses of possibility applies to necessary and must as well. "A square must have four sides" and "it is necessary that a square has four sides" express logical necessity. Whereas "you must be 18 to vote in Australia" is obviously about legal rather than logical necessity. 4.6

EXCLUSIVE AND EXHAUSTIVE POSSIBILITIES

Apart from talking about the ways in which something is or is not possible, there are also some useful terms for talking about the connections between different possibilities. First, we can speak of a possibility including another. There being rain tomorrow includes the possibility of a heavy rainstorm, and the possibility of just a light drizzle. Second, one possibility can exclude another. If Cinta is in Spain right now, that excludes the possibility that she is in Brazil. Finally, two possibilities can also be independent of each other. Whether it will rain tomorrow presumably does not depend on what you ate for breakfast this morning. The word exclusive is sometimes used to talk about one possibility excluding another, and it is important not to confuse exclusive with exhaustive. • A set of possibilities is exhaustive when at least one of them obtains in any logically possible situation (they do not leave out any situation). • A set of possibilities is exclusive when there is no logically possible situation in which more than one of them obtains (the truth of one excludes the truth of the others). • In other words, if a set of possibilities is both exhaustive and exclusive, then in any logically possible situation, exacüy one of them obtains. This explanation might be a bit too abstract, so here is an illustration. Suppose x is an integer:

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• Two possibilities that are neither exhaustive nor exclusive: x > 3, x > 4. They are not exhaustive because the possibility that x = 2 is not included. They are not exclusive because both of them can be correct, as when x > 5. • Exhaustive but not exclusive: x > 4, x < 10 • Exclusive but not exhaustive: x> 4, x = 1 • Exclusive and exhaustive: x > 0 , x = 0, x < 0

EXERCISES 4.1 Suppose we have a definition X=Y. Are the following statements correct about this definition? Why or why not? a) If the definition is too wide, then X is not necessary for Y. b) If the definition is too wide, then Y is not necessary for X. c) If the definition is too narrow, then X is not sufficient for Y. d) If the definition is too narrow, then Y is not sufficient for X. e) If X is not necessary for Y, then the definition is too wide. 4.2

Are these statements true or false? a) If X is logically sufficient for Y, and Y is logically sufficient for Z, then X is logically sufficient for Z. b) If X is logically necessary for Y, and Y is logically necessary for Z, then X is logically necessary for Z. c) If X is not necessary for Y, then Y is not necessary for X. d) Being an intelligent student in the class is necessary for being the most intelligent student in the class. e) If something is not logically impossible, then it is logically possible. f) If something is empirically impossible, then it does not actually happen in the world. g) If something is empirically possible, then it actually happens in the world. h) If something actually happens in the world, then it is empirically possible. i) If something is logically possible, then it is empirically possible. j) If something is empirically possible, then it is logically possible. k) If something is empirically possible, then it is technologically possible.

4.3 A definition of X provides necessary and sufficient condition for X. See if you canfillin the blanks below correctly with necessary condition or sufficient condition: a) If the definition is too wide, this means the definition fails to provide the correct for X. b) If the definition is too narrow, this means the definition fails to provide the correct for X.

EXERCISES

4.4

39

Determine whether these possibilities are exhaustive and/or exclusive. a) Inflation goes up. Inflation comes down. b) P and Q. Neither P nor Q. c) Sadie and Rita are happy. Sadie and Rita are sad.

4.5 Many management and law school admission tests include questions known as "data sufficiency questions." There are also similar questions in many recruitment exams. So do try out the following questions. You will be given some information, and then you have to pick the correct answer out of the five choices listed below: 1. Statement 1 alone is sufficient to answer the question, but statement 2 alone is not sufficient. 2. Statement 2 alone is sufficient to answer the question, but statement 1 alone is not sufficient. 3. Both statements are necessary for answering the question, and neither statement alone is sufficient. 4. Either statement by itself is sufficient to answer the question. 5. Statements 1 and 2 together are not sufficient to answer the question. a) Three stones have a combined weight of 40 kilograms. What is the weight of the heaviest stone? Statement 1: One stone weighs 10 kilograms. Statement 2: One stone weighs 20 kilograms. b) Two students joined the same company at the same time. How much more money per month does trainee X now earn than trainee Y? Statement 1 : Y earns $3000 per month more than when he first started. Statement 2: X earns $5000 per month more than when she first started. c) What is the total number of cakes that Elia and Maddalena have eaten? Statement 1: Elia ate twice as many cakes as Maddalena. Statement 2: Maddalena ate two cakes fewer than Elia. 4.6 Describe the mistake in this argument in terms of necessary and sufficient conditions: Students who do not study always fail the exam. Since I have studied, it follows that I will pass the exam.

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CHAPTER 5

LINGUISTIC PITFALLS

Linguistic pitfalls are inappropriate uses of language that hinder accurate and effective communication. This can happen when we use language that is unclear, distorted, or empty in meaning. We now look at these situations one by one. 5.1

UNCLEAR MEANING

Lack of clarity can arise in many ways. The words we use might be ambiguous or imprecise or the meanings are incomplete. But it can also be due to the failure to organize ideas properly. 5.1.1

Ambiguity

An ambiguous expression is one with more than one meaning or reference. There are different kinds of ambiguity. Lexical ambiguities are cases where a single word or name has more than one meaning in a language—for example, deep ("deep insight" vs. "deep tunnel") and bank ("river bank" vs. "investment bank") and words like light and over. Consider also Japanese teacher, which might mean a teacher from Japan or anyone who teaches Japanese. Even place names can be An Introduction to Critical Thinking and Creativity: Think More, Think Better. By Joe Y.F. Lau Copyright © 2011 John Wiley & Sons, Inc.

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ambiguous. Angkor Wat is commonly used to refer to the beautiful historic site in Cambodia containing lots of temples built by the Khmer monarchs. But Angkor Wat is also the name of just one specific temple (the largest one) in the whole area. Referential ambiguity arises when the context does not make it clear what a pronoun or quantifier is referring to. • John hit Peter with his iPhone. Then he died. (John, Peter or someone else?) • Amie and Lusina gave some cookies to Delman and Michelle because they liked them. Syntactic ambiguity occurs when there is more than one way to interpret the grammatical structure of an expression. This can happen even when the meanings of the individual words are clear. • Ralph saw Sharon on the roof with a telescope. (Did Ralph use a telescope or did he see Sharon carrying one on the roof?) • The students were told to stop partying at midnight. (Were they told not to hold midnight parties or were they told at midnight not to party anymore?) • Visiting relatives can be boring. (Are the visiting relatives boring or is it boring to visit relatives?) To remove ambiguity, we can rewrite our sentences so that they are no longer ambiguous. Or we can list all the different interpretations. This process is called disambiguation. Take the famous Zen question, "If a tree falls in a forest and no one is around to hear it, does it make a sound?" We can point out that sound is lexically ambiguous—it might mean a physical vibration through some medium such as air, or it might mean an auditory conscious experience. When no human being or animal is around, the falling tree would make a sound in the first but not the second sense. It is important to be able to spot ambiguity in evaluating arguments. Equivocation occurs when a key term changes meaning in the middle of an argument. Consider this argument against equality from Murray N. Rothbard, a libertarian author and economist: The diversity of mankind is a basic postulate of our knowledge of human beings. But if mankind is diverse and individuated, then how can anyone propose equality as an ideal? Every year, scholars hold Conferences on Equality and call for greater equality, and no one challenges the basic tenet. But what justification can equality find in the nature of man? If each individual is unique, how else can he be made "equal" to others than by destroying most of what is human in him and reducing human society to the mindless uniformity of the ant heap? (Rothbard, 2010) On the face of it, the argument seems plausible. If equality is unattainable or undesirable, it would be wrong to call for more equality. But the apparent plausi-

UNCLEAR MEANING

43

bility rests on an equivocation between two meanings of equality. The argument starts by saying that equality cannot be an ideal. This is correct if equality means everyone being physical identical, having the same appearance, personality, and so on. This form of equality is indeed undesirable if not impossible to achieve. It is a good thing there is diversity and individuality, but nobody wants to get rid of that. When the argument goes on to talk about scholars calling for greater equality, these people are talking about a different notion of equality—people having the same basic rights and equal opportunity. Two people can be very different, but they can still enjoy the same basic rights such as the right to free speech and freedom of religion. Once we distinguish between the two senses of equality, the argument is not so plausible—the fact that equality is impossible in one sense does not imply that equality in the second sense is undesirable or unachievable. Perhaps the author believes that there is a connection between these two senses of equality. But that would require a very different and more detailed argument. 5.1.2

Vagueness

A term is vague if it has an imprecise boundary. A sunny room is no longer bright when the sun is gone. But as the sun sets, there is no point in time when the room suddenly changes from being bright to not bright. So bright is vague. Tall is also vague since there are borderline cases where it is impossible to say whether the person is tall or not, even when we know that person's exact height. The meaning of tall is just not precise enough. If you think about it, probably most words in our language are vague in some way—for example, mountain, clever, and smelly. Strictly speaking, vagueness is different from ambiguity. A term can be vague even though it is not ambiguous, such as the Atlantic Ocean. An ambiguous term might have very precise meanings. For example, a billion is normally taken to be one thousand million, but some people take it to mean one million million. So billion is ambiguous, but the two possible meanings are very precise! Vagueness in a statement decreases the amount of information that is being conveyed. Consider these statements in increasing order of vagueness: 1. Five men and two women suffered from minor bruises in the accident. 2. A few men and women suffered from bruises in the accident. 3. A few people were hurt in the accident. When a statement is more precise, it contains more details and runs a higher risk of being wrong. If it turns out that only four men were hurt in the accident, the first two statements will be false but the third one is still true. So being vague can be useful if we want to be evasive or to avoid being wrong. But it also means we should be careful of vague statements that carry no useful information. Politicians are of course very good at this game, promising to do this or that when time is right but without saying what counts as the right time. Similarly, horoscope entries are full of useless and vague predictions. A typical one might say: "Be prepared for a

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change of direction this week". But what counts as a change of direction? Does it include someone blocking your way so you can't walk in a straight line? Without more concrete clarification, we can easily find one event or another as "evidence" that confirms the prediction. So it is important to avoid vagueness in situations that require concrete information. In job applications, for example, employers usually want clear evidence of your abilities and achievements. Numerical facts can get the point across quickly. In your CV instead of vague general statements such as "responsible for writing user guides," it would be more impressive to say "wrote five program manuals for 7,000 customers within one week." The point is not to throw in as much information as possible but to highlight concrete achievements. 5.1.3

Incomplete Meaning

The following question appeared in an aptitude test for primary-school children in Hong Kong. You are supposed to pick the odd one out: apple, banana, watermelon, orange, pear Such questions are common in IQ tests, but they often test the ability to secondguess the examiner rather than true intelligence. This is because these questions do not have correct answers. The official answer to the question above is "banana", presumably because its shape is the least spherical. But one could equally have picked "watermelon", because it is the only vine crop on the list; or "orange", because it is the only one with an orange color! The point is that it does not make sense to judge whether two things are similar or different, unless we say how they should be compared. A raven is like a writing desk in that they are both smaller than a mountain, but they are also not like because only one is a bird. Terms like similar, same as, different, usefiil, better, and importanthave incomplete meanings. They presuppose certain standards of comparison, and their meanings are unclear if the standards are not specified. Is love more important than a banana? It depends whether you are trying to cure loneliness or distract an attacking gorilla. In some situations, the standard of comparison is clear even if it is not made explicit. If someone looks at two identical twins and says they are exactly alike, he is probably saying that they look similar. But sometimes the standard of comparison can be totally lacking. A breakfast cereal advertisement might say: "A healthier alternative for your family." But healthier compared to what? Surely not healthier than all other alternatives for breakfast. Without a meaningful comparison, the claim has no concrete content at all.1 1 It might be suggested that the same is true of the subtitle of this book: "Think More, Think Better". More than what and better than what? But the natural interpretation in this context is that our think improves as a result of learning more about critical thinking and creativity.

DISTORTION

5.1.4

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More global defects

Ambiguity, vagueness, and incomplete meaning occur at the level of words or sentences. But lack of clarity can also happen at a more global level. If an article lacks a coherent structure or the connections between the sentences are unclear, it will be difficult to understand the article as a whole, even if the individual sentences are relatively clear. The same applies to a lecture or a presentation. To avoid this problem, it is crucial to plan ahead and organize the ideas using a good framework. (See the discussion in Section 2.3.) 5.2

DISTORTION

5.2.1

Inappropriate emotional connotation

Distortion is a matter of misconstruing the meaning of words, such as giving an incorrect reportive definition. Another typical example is the use of inappropriate emotive connotations. Many linguistic expressions are not purely descriptive but carry positive or negative connotations. Describing someone as "generous" is to portray that person in a positive light. However, sometimes people attach emotional connotations to words that do not have any. Or they try to choose words with a particular connotation to get people see things their way. Here are some examples: • Defining religion as a superstitious belief in the existence of God. • Insisting on calling a mistake as a valuable learning opportunity. • Trying to be diplomatic by saying that someone is genuinely interested in other people rather than being nosy. In everyday life, it is not easy to avoid using terms that carry connotations of one kind or another. Whether you describe a person as "independent" or "uncooperative" reflects your judgment of the person. As we can see from the last two examples, choosing words with the right emotional connotations can serve useful social purposes like saving face or maintaining politeness. But the first example is more objectionable because it injects the wrong kind of emotional connotations. Even if it is irrational to believe in a religion, this is something to be argued for independently and not by stipulation. To sum up, we should be alert to the connotations of the words that we use and be careful of attempts to use such connotations to bias our perception. 5.2.2

Weasel words

The use of weasel words is also an example of distortion. These are cases where the ordinary meaning of a word is changed inappropriately in the middle of a discussion, usually in response to some counterexample or an objection. Take the following exchange:

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BILLY : All politicians are corrupt. KATE : What about Nelson Mandela and Vaclav Havel? They are well-respected politicians with integrity. BILLY : They are not corrupt, so they are not real politicians. Billy seems to be suggesting that a person cannot be a "real" politician unless that person is corrupt. But a real politician is just the same as a politician and both Mandela and Havel have been presidents of their own countries and active in political affairs, so there is no reason why they should not be considered as politicians. The other problem is that if politicians have to be corrupt, Billy's claim that all politicians are corrupt becomes empty and uninteresting claim, since he is in effect saying that "all corrupt politicians are corrupt." But Billy's maneuver is not atypical. Many people try to distort the meaning of a term X by making similar stipulations about what a "real X" must be like. 5.2.3

Quoting out of context

Distortion includes misrepresenting what other people have said, deliberately or not. A movie critic might say sarcastically, "This is a fantastic movie, if you are brain dead." A disingenuous advertisement might then quote the critic as saying "a fantastic movie"! This way of quoting out of context is unfortunately quite common. For example, some people who object to evolution use this passage to argue that Charles Darwin (1809-1882) himself had doubts about evolution: To suppose that the eye with all its inimitable contrivances for adjusting the focus to different distances, for admitting different amounts of light, and for the correction of spherical and chromatic aberration, could have been formed by natural selection, seems, I freely confess, absurd in the highest degree {On The Origin of Species, Ch. VI). But this is again quoting out of context, because Darwin went on to say we should not reject a scientific theory simply because it goes against commonsense, and that the complex eye in fact could have evolved slowly and gradually starting from simple light-sensitive cells. But unless you look up the origin text, you might be misled into thinking that Darwin had reservations about his own theory. Similarly, in 2009, the British Homeopathic Association presented material to the British Government claiming that there is scientific evidence supporting the effectiveness of homeopathic therapy.2 For example, it quoted the following conclusion from a research paper: There is some evidence that homeopathic treatments are more effective than placebo. 2

Homeopathy is a form of alternative medicine that treats illnesses using solutions that are supposed to become more potent when they get more and more diluted, even to the point where the amount of active ingredient is negligible according to mainstream science.

DISTORTION

47

Encouraging right? But read the full paragraph where the quote comes from: There is some evidence that homeopathic treatments are more effective than placebo; however, the strength of this evidence is low because of the low methodological quality of the trials. Studies of high methodological quality were more likely to be negative than the lower quality studies. Further high quality studies are needed to confirm these results (Cucherat et al., 2000). So it turns out that the researcher's conclusion is just the opposite of the initial impression! Unfortunately this kind of selective quotation, or quote mining, is very common. We have to be very careful and if we are suspicious we should try and look up the original sources ourselves. 5.2.4

Category mistake

A category mistake also distorts meaning. This is to assign a property to an object when it is logically impossible for an object of that kind to have the property in question. The famous linguist Noam Chomsky gave a well-known example of a grammatical yet incoherent sentence: Colorless green ideas sleep furiously. Since an idea is not the kind ofthing that can sleep or have a color, the sentence exemplifies the category mistake. Similarly, take the slogan "Information wants to be free." The first problem with this statement is that it is ambiguous because free can either mean "easy to access" or "does not costing anything". More important, the sentence anthropomorphizes information as an agent that can want things to happen, which is a category mistake. Information does not and cannot want anything; people do. So it is not clear what the sentence really means. Does it mean most people want information to be free? But that is simply not true. In general we are reluctant to publicize information about sensitive financial or private matters. Perhaps a better interpretation of the statement is that once released, information tends to spread around and cannot be contained. Sometimes category mistakes are the results of careless writing or bad grammar. A student might write in a hurry, "Procrastination is a person who keeps putting off what he should do." Interpreted literally, this sentence is logically false, because procrastination is a character trait or a habit, not a person. But the intended meaning is clear enough. Reincation is a type of category mistake. The word reify came from the Latin word res, which means "thing". Reincation is treating an abstract idea or property as if it were a concrete physical object. Take "The truth wants to be told." It treats truth as if it were a person who wanted things to happen, which is impossible. But it is not hard to guess what the speaker is trying to say. Maybe she is saying it is important to tell the truth, or perhaps she thinks people will be interested to know the truth. Similarly, the Cuban leader Fidel Castro said "History will absolve me" when he was on trial at some point. But history is not a person who can forgive or

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absolve anybody. Presumably he was saying that people will eventually agree with what he had done. These two examples show that reification in itself need not be objectionable. It increases dramatic impact and is a useful literary device. But if a claim that involves reification constitutes a meaningful and informative claim, it can be usually be expressed more clearly without using reification. When it is difficult if not impossible to carry out this translation, this is a good sign that the original statement does not actually have a clear meaning. So, in general, better avoid reification unless you want dramatic impact. If you have to use it, make sure you know what you really want to say.

5.3

EMPTY MEANING

Empty meaning is a case in which words are used without serving any useful purpose or providing little information. For example, careful analysis often requires drawing subtle distinctions. Earlier in this chapter we distinguished between two senses of equality. But sometimes people try to make a distinction and fail. If so the distinction is empty, a distinction without a difference. Here are two examples: • "We must follow God's will, and not what we or other people think God wants us to do." This distinction is empty because there is no way to follow God's will other than to follow what we or other people think is his will. • Enjo kösai means "compensated dating" in Japanese. The practice started in Japan (and has now spread to many countries) and involves men giving money to young girls in exchange for companionship and sometimes even sex. Many people insist it is not prostitution, but if sex is involved, the distinction is but an empty one. 3 Questions can also be empty when they serve no useful purpose. Form I-94W is filled out by many non-U.S. citizens when they enter the United States. The form includes questions such as, "Are you now involved in espionage or sabotage or in terrorist activities?" and "Are you seeking entry to engage in criminal or immoral activities?" Surely we do not expect spies or criminals to answer truthfully, so it is not clear why such questions are needed. Someone who answers yes is probably a little bit crazy, so maybe that is the real purpose of the questions! Apart from empty questions, there are also empty statements. These are claims that purport to provide useful information, but fail to do so in the relevant context. Sometimes this is because the statements are analytic. They are trivially true in virtue of their meaning, and as a result they provide no concrete information about the world. (See also Section 6.3.) Consider this weather forecast: Of course, someone in such a situation might feel betterby believing that one is engaged in compensated dating and not prostitution. But that would be a kind of self-deception. 3

EMPTY MEANING

49

Either it will rain tomorrow or it will not. If it rains tomorrow, then precipitation will occur. There might or might not be a heavy overcast tomorrow. But if there is a heavy overcast that lasts the whole morning, then it will not be a very sunny morning. You can see that these empty statements fail to make any definite prediction about tomorrow's weather. They will be true whatever the weather is like the next day. These sentences are all analytic and in this context they convey no concrete information at all. Or consider the slogan "survival of the fittest", often used to describe Darwin's theory of evolution.4 Some people criticized the claim by saying that fittest just means "those which survive." So the whole claim becomes "those which survive, survive," which is of course empty and trivially true. Fortunately this is not an accurate description of the theory of evolution. Otherwise it would be in deep trouble! It should be pointed out that it is not a mistake in itself to use analytic statements. They are important to logic and mathematics, and they play a useful role in language learning. "Bachelors are unmarried men" is analytic and conveys no empirical information about bachelors—for example, how many bachelors there are or whether they are happy. But obviously this statement is useful for people studying English. Analytic statements can also convey useful conversational implicatures. Suppose Helen asks whether Francine will come to the party, and Francine replies, "If I come, I come." This empty reply does not answer the question at all, but it shows that the speaker is hesitant and does not want to commit herself. Similarly we often use analytic statements to express uncertainty or to emphasize the available options. If we don't know whether a proposal will be successful, we might say "this might or might not work" as a qualification. Or if we want to remind an indecisive person to make up his mind, we might say something like, "Either you do it or you don't." These are not cases of linguistic pitfalls since they serve to convey useful conversational implicatures. Not all empty statements are analytic. Some empty statements are nonanalytic and do have some empirical content. But we still say they are empty because the information they provide is too trivial or obvious. For example, in many debates people want to appear to be insightful and they might say something like "X cannot solve all problems." Here, X might be democracy, technology, science, the government, money, punishment, and so on. These claims are typically empty because they are unlikely to be seriously disputed by anyone. For example, democracy cannot prevent natural disasters from happening or stop people from getting cancer, so it cannot solve all problems. But when people are debating whether a country should adopt democracy, the real issue is whether democracy is better than other systems of governments. The charge that democracy cannot solve all problems is an empty and irrelevant criticism. 4

It was actually coined by the philosopher Herbert Spencer (1820-1903).

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5.4

LINGUISTIC PITFALLS

GOBBLEDYGOOK EVERYWHERE

The word gobbledygook was coined by Texan lawyer Maury Maverick in 1944 to describe obscure and convoluted language full of jargon.5 It is an extreme form of linguistic pitfalls, where simple ideas are made unnecessarily complicated and cliches are dressed up as profound truths. Yet they can be found everywhere. Here are two samples from actual business writing (BBC News, 2003): • The benefit of having dedicated subject matter experts who are able to evangelise the attributes and business imperatives of their products is starting to bear fruit. • I admire your focused attention to screening the quantum of remaining potentiality vs. the generic strategic quantum of growth potentiality that we are now trying to seek access to. Many people seem to think that long strings of management jargon indicate sophistication and professionalism. But in fact they hinder communication and are unnecessarily long winded. The first sentence just says that using experts to promote their products is bringing benefits. The second one is rather incomprehensible. Perhaps the writer is just saying "I admire you for making the best of what we have." Legal documents also contain a lot of gobbledygook. Consider this piece of real traffic regulation: No vehicle shall be turned so as to proceed in the opposite direction within an intersection, or upon any street in a business district, or upon a freeway, expressway or controlled-access highway, or where authorized signs are erected to prohibit such movement, or at any other location unless such movement can be made with reasonable safety to other users of the street and without interfering with the safe operation of any traffic that may be affected by such movement. The sentence is certainly verbose—"that may be affected by such movement" is redundant, and why not "U-turn" instead of "turned so as to proceed in the opposite direction"? The sentence is also way too long and creates confusion. In particular the scope of unless is not clear—is the sentence saying that a U-turn is not allowed anywhere unless it is safe to do so, or is it saying that a U-turn is absolutely prohibited in those places listed, and otherwise only when it is safe? Eliminating gobbledygook and adopting plain language is not solely a matter of style and preference. There are practical benefits as well. Legal documents are supposed to provide guidance, and clear language helps citizens understand their rights and duties. For many organizations, employees make fewer errors when documents and instructions are written in plain language. Clients have fewer en5

It is amusing that gobbledygook is the language of the goblins in the Harry Potter book series.

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51

quiries and complaints, and they are more satisfied. Plain language is also important for consumer protection when they purchase products and services. This is not to say that linguistic complexity and specialized vocabulary are always bad. Some ideas are complicated, and technical terms make it easier to communicate ideas among professionals. The problem comes when buzzwords are used to obscure, hide, or inflate ideas and actually hinder accurate and effective communication. Let us end with this list of jargon, and see if you can guess what each phrase means: • Terminate with extreme prejudice. • Spontaneous energetic disassembly. • Collateral damage. • Wooden interdental stimulator. • Negative patient care outcome. EXERCISES 5.1

If any statement below is ambiguous, list all its possible interpretations. a) Here is the photo of the model everyone is talking about. b) Park the car next to the tree in front of the house. c) The new CEO promised to avoid layoffs during the merger. d) For sale: 10 puppies from an Australian terrier and a Boston terrier. e) Lack of Brains Hinders Medical Research (newspaper headline). f) Being able to think clearly helps us learn better. g) Students who play video games often have poor grades. h) Bring your birth certificate or your passport and your identity card. i) I stored my antique watch in the safe deposit box in the bank, but the river flooded the bank and the watch was ruined.

5.2

Identify the category mistakes below and rewrite the sentences properly. a) A comedy is when lots of funny things happen. b) Dr. Tran will talk about the experience of civil engineering in Vietnam in tomorrow's seminar. c) The students in my class are smarter than the other classes.

5.3

Simplify these sentences as far as possible. Avoid changing their meaning. a) Talking to Ann has induced Peter to generate the idea of building a house. b) Our educational system at the moment is predicated on the assumption that lectures are enjoyed by students.

5.4

Discuss the linguistic pitfalls in these passages, if there are any. a) Law graduates of the university have a higher income. b) Rita got the flu from a kid who was ill four days ago.

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c) Our cookies are tastier with 20% more butter. d) This is the saddest day of my life since I got married. e) Some people say that discrimination is morally wrong. But this is just hypocritical. First, we treat people differently all the time. We give higher pay to those who are more capable, and we like our friends better than strangers. Also, we actually praise people for being discriminating — in their taste for good food, wine and music, for example. So it is just plain wrong to get so worked up about discrimination. f) A harmful truth is better than a useful lie. (Thomas Mann) 5.5 IS1 Are these statements empty? What do you think the speaker is trying to convey, if anything? a) Art is art. Everything else is everything else. (Ad Reinhardt) b) What will be, will be. 5.6

E3 What do you think these statements mean? a) The Internet treats censorship as damage, and routes around it. (Programmer and computer activist John Gilmore) b) Nature abhors a vacuum.

5.7 Ë3 Enjoy these famous quotes attributed to some famous people. What do they have to do with linguistic pitfalls? a) Smoking kills. If you're killed, you've lost a very important part of your life. (Actress Brooke Shields ) b) You wouldn't have won if we'd beaten you. (Baseball player Yogi Berra) c) You've got to be very careful if you don't know where you are going, because you might not get there. (Yogi Berra) d) I do not like this word bomb. It is not a bomb. It is a device that is exploding. (Former French ambassador Jacques le Blanc on nuclear weapons.) e) Traditionally, most of Australia's imports come from overseas. (Former Australian cabinet minister Keppel Enderbery) f) I have the body of an eighteen-year-old. I keep it in the fridge. (Irish comedian Spike Milligan) g) I don't diet. I just don't eat as much as I'd like to. (Supermodel Linda Evangelista) h) When more and more people are thrown out of work, unemployment results. (Calvin Coolidge, the 30th President of the United States)

CHAPTER 6

TRUTH

The concept of truth is one of the most basic concepts in logic. There are certainly lots of controversies in philosophy about the nature of truth. However, for the purpose of critical thinking, we can adopt Aristotle's definition: To say of what is that it is not, or of what is not that it is, is false, while to say of what is that it is, and of what is not that it is not, is true. (Metaphysics, 1011b25) The basic idea here is that truth is a matter of correspondence to reality. If you say "Paris is in France," then your statement is true since Paris is indeed in France. Whereas "Paris is in Japan" is false since it is not the case. When a statement is true, logicians like to say that it has T (truth) as its truth-value. When a statement is false, its truth-value is F (falsehood). If a statement is neither true nor false, then we say it lacks a truth-value. 6.1

RELATIVISM

Aristotle's simple definition does not imply we can always discover the truth. The sentence "Aristotle ate an odd number of olives during his life" is either true or An Introduction to Critical Thinking and Creativity: Think More, Think Better. By Joe Y.F. Lau Copyright © 2011 John Wiley & Sons, Inc.

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false, but we would never know. Something can be objectively true even if nobody knows it or if people disagree about it. Objectivity is also quite compatible with changes in beliefs over time. People in the past used to think that the Earth is flat. But we no longer believe that. This change in perspective does not mean that truth is a matter of perspective. Relativism is the view that there is no objective truth, that truth is always a matter of perspective or opinion. However, this extreme position is difficult to defend. Consider the question of whether relativism itself is true in an objective way or a relative way. If the former, then there is at least one objective truth and so relativism is inconsistent. It might be said that perhaps everything is relative except relativism itself. But why should there be such an exception? Why not allow other truths to be objective as well? If relativism is objectively true, then presumably "Either relativism is true or 1 + 1=2" is another objective truth. So there cannot be just one objective truth! On the other hand, if relativism is true only relative to some perspectives, then it is not clear why it should be accepted, since it is also false relative to other perspectives. In any case, we might also wonder whether anyone is sincerely a relativist about all truths. Suppose we ask a relativist to jump off a plane without a parachute. Unless it is objectively true that he is likely to die, it is not clear why he should refuse. If everything is relative, then the prediction that he will not die is just as true (relative to some perspective) as the prediction that he will die (relative to another perspective). There are other restricted forms of relativism that are milder and perhaps more plausible. These theories say that only certain types of truths are relative, not that all truths are. For example, relativism about taste is not implausible. Some people think warm beer tastes better than cold beer and others disagree. Is there a correct answer or is it a matter of preference? If the latter, then this suggests that relativism about taste is true. But of course, this is quite compatible with the existence of objective truths outside the area of taste.

6.2

STATEMENTS

So far we have not said much about the kind of things which are supposed to be true or false. For the purpose of this book we focus on statements, which can be used to express or formulate claims, hypotheses, theories, propositions, beliefs, knowledge, and so on. We shall define a statement as a declarative sentence. In English, there are three main sentence types: lype

Main function

Example

declarative

make assertion

Amie is here.

interrogative

ask question

Is Amie here?

imperative

issue request or command

Come here, Amie!

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As you can see, a declarative sentence is a complete and grammatical sentence that makes a claim. So here are some examples of statements in English: • Time flies. • The sky is dark and it will rain soon. • Everyone knows that the moon is made of green cheese. • The data and information provided on this web page is for informational purposes only and is not intended for trading or commercial purposes, unless written prior permission is obtained by the user from the author, though the author will not be liable for any errors or delays in the content, or for any actions taken in reliance thereon. Statements can be true or false, short or long. But they must be grammatical and complete sentences. A good test of whether something is a statement is that it should still be grammatical if you add "it is true that" to the beginning of the statement—for example, "It is true that time flies." These, however, are not statements: • The United Nations (A proper name, but not a sentence.) • Poker face (Not a complete sentence.) • Is it raining? (Not a declarative sentence.) • $,L©$,J§t:L£ (A meaningless string of symbols.) 6.3

TYPES OF TRUTH

We spend a lot of time trying to find out whether certain things are true or not. It would help if we understand better the nature of three different kinds of truths: Type of statement

True

False

analytic

Every triangle has three sides.

All bachelors are married.

empirical

Some apples are green.

All birds can fly.

value

We should not torture babies.

We should torture babies.

An analytic truth is a statement that is true solely in virtue of the meaning of the words contained in the statement. Likewise, an analytic falsehood is a statement that is false solely in virtue of the meaning of the words in the statement. In both cases, what makes them true or false depend solely on the meaning of words and not other kinds of facts about the world. "Every triangle has three sides" is analytically true because of the definition of triangle. If you fully understand the meaning of the sentence, you will know that it is necessarily true. This is purely a

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matter of linguistic convention. You do not need to look at all the different triangles one by one and count the number of sides they have. On the other hand, the truth and falsity of an empirical statement depends on contingent facts about the world, facts that could have been different if the history and physical laws of the universe had been any different. Knowing the meaning of the sentence "lohn is a bachelor" is not sufficient for knowing whether the sentence is true. You need to actually check John's marital status, perhaps in a government registry. Generally speaking, to find out whether an empirical statement is actually true, we need empirical observations or scientific studies. A value statement is one about what is be good or bad, what is morally right or wrong, or what we should or should not do. Value statements seem to be distinct from empirical statements because people can agree about all the facts and still disagree about what is good or bad. They also do not seem to be analytic because people might understand the meaning of a controversial value statement perfectly well and still disagree about its truth. (We shall talk more about value statements in Chapter 18.) 6.3.1

Analyzing questions and issues

There is actually a lot more to be said about the distinction between these three kinds of statements.1 But for the purpose of everyday critical thinking, the distinction as presented here should be adequate. It is important not to confuse the three types of statements because they require different sorts of evidence to argue for or against them. This will help us analyze a complicated issue by breaking it down into three types of questions: questions about meaning, questions about empirical facts, and questions about values. Examples: • Which is the world's largest bank? To answer this question, we need to break it down into a question about meaning and a question about empirical facts. First, we need to clarify what is meant by largest, because there are different ways of measuring the size of a bank—for example, assets, market value, profit. One we have denned what largest means, which is the largest bank becomes an empirical question. In 2010, China's ICBC was the largest bank according to market value. But if we rank in terms of total assets then the Bank of America might be the world's largest bank instead. • Should there be a minimum wage? Not every country has legislation mandating a minimum wage for workers. Is this something desirable? This question combines issues about meaning, empirical facts, and values. First, what do we mean by minimum wage'? How is the wage level determined? 1 There are lots of philosophical controversies about the concepts mentioned. For example, it has been argued that there is no sharp distinction between analytic and empirical statements. Also, many philosophers believe there are empirical statements that are neither analytic nor contingent. It has also been argued that some analytic statements are not necessarily true, even though they are true in virtue of meaning. Many people would also argue that value statements are neither true nor false.

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57

Does it apply to temporary or part-time workers? Then there are empirical questions about the legal, economic, and social consequences of introducing minimum wage. Does it have any effect on unemployment? Does it increase inflation or layoffs? Does it affect economic competitiveness? How does it affect those who are least well off? Finally there are questions about values. What ought to be the role of the government in the labor market? How important is the freedom of contract? Is the imposition of a minimum wage consistent with justice, equality and fairness? As we can see from these two examples, many complicated questions can be broken down into further questions along the three dimensions of meaning, facts, and values. This provides a systematic approach to analyze complicated issues. EXERCISES 6.1

Discuss these arguments. a) Relativism is correct because any true sentence can be changed into a false one if you give it a different meaning, say changing "1+1=2" to mean "The Moon is made of tofu." b) Different people have different opinions. So relativism is obviously true. c) If relativism is false, then certain things are objectively true. But we never have direct access to objective reality. Our theories are inevitably our conceptual constructions, and they are always a product of our existing culture and perspectives.

6.2

Which of the following are statements? a) Cats and dogs. b) Yummy ramen noodles! c) Is ramen yummy? d) Ramen is yummy. e) Go away and never come back. f) The unexamined life is not worth living. g) If ramen is yummy, then sushi is even more yummy. h) Ramen is popular not just in Japan.

6.3

Classify these statements as analytic, empirical or value statements. a) There are more rainy days in Shanghai than sunny days. b) Violence causes more violence. c) Many people believe that greed is good. d) People should be required to donate their organs when they die unless they have explicitly indicated otherwise. e) If Peter was killed yesterday, then Peter is now dead. f) All purple things are colored. g) Helping people makes us happier. h) Critical thinking is something people ought to pursue.

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i) If Rebecca is Shannon's mother, then Shannon is Rebecca's offspring. 6.4 E3 What is your opinion about the following questions? List the conceptual, empirical, and value issues that should be considered. a) Governments should subsidize industries that develop renewable energy. b) Softdrinks should not be allowed in schools.

CHAPTER 7

BASIC LOGIC

7.1 SOME BASIC CONCEPTS Many people associate logic with brain teasers and mathematical puzzles, which seem to have little relevance to real life. The truth is that logic is of great practical significance. If your friend is in New Zealand, you know she is not in Japan. This piece of everyday reasoning involves logic. The core of logic is about consistency and deduction, both of which are indispensable for everyday thinking, not to mention scientific research and legal reasoning. Logic also plays a special role in computer technology. Computers are good at processing information because their processors can perform a huge number of logical operations very quickly. Obviously, normal people are capable of logical reasoning to some extent, or else we would not be able to survive very long! But making the effort to study some logic can improve our understanding of what good reasoning is like so we can become even better. In this chapter we shall look at some basic concepts of logic.

An Introduction to Critical Thinking and Creativity: Think More, Think Better. By Joe Y.E Lau Copyright © 2011 John Wiley & Sons, Inc.

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7.1.1 Consistency A set of statements is consistent when and only when it is logically possible for all of them to be true in the same situation. Otherwise they are inconsistent. So for example, "Adrian is happy" and "Adrian is married" are consistent with each other since there is no reason why a married person cannot be happy. On the other hand, "Visanna is 30 years old" and "Visanna is 20 years old" are obviously inconsistent. Here are a few more points to remember about consistency: • Inconsistent statements are also known as contraries. • We can also speak of a single statement as consistent or inconsistent, depending on whether it is logically possible for it to be true. "There are round squares" is inconsistent and false. "Paris is in France" is consistent and true. "Nobody lives in Paris" is consistent but false. • Whether a set of statements is consistent depends on whether it is logically possible for all of them to be true in the same situation. It is not necessary that they are actually true. "Paris is in Italy" and "Nobody lives in Paris" are consistent with each other, even though both are actually false. • To show that a set of statements is consistent, we can either show that they are actually true or describe a logically possible situation in which they are all true. Consider the two previous statements about Paris. Imagine that Italy conquers France with chemical weapons and takes over Paris. But Paris became contaminated and everyone leaves. This imaginary situation is farfetched but coherent, and shows that the statements are consistent. • Statements that are actually true are consistent with each other, but false statements might or might not be consistent with each other. The two previous statements about Paris are false but consistent. "Nobody lives in Paris" and "Only 10 people live in Paris" are false and inconsistent with each other. • If a set of statements is inconsistent, the statements will entail a contradiction of the form: P and it is not the case that P. Take "Nobody lives in Paris" and "Only 10 people live in Paris." The second statement entails "It is not the case that nobody lives in Paris," and together with the first statement they entail the blatant contradiction: Nobody lives in Paris and it is not the case that nobody lives in Paris. Many inconsistencies are easy to detect, but not always. Suppose someone says we should be cautious in making general claims. This seems like good advice because sweeping generalizations like "Every Italian loves pizza" and "All Belgian chocolates are good" are bound to have exceptions. So we might be tempted to

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conclude that all general claims have exceptions. But the claim "All general claims have exceptions" is actually inconsistent. It is itself a general claim, and if it were true, it should also have an exception. But this implies that not all general claims have exceptions. In other words, the claim cannot possibly be true and is therefore inconsistent! If we want to speak truly, we should avoid inconsistent statements. But sometimes ordinary speakers use sentences that seem to be inconsistent, such as,"I am happy and I am not happy." Why do people say things that cannot be true? One answer is that these sentences have incomplete meaning. When we fully specify their meaning, they are no longer inconsistent. For example, perhaps the speaker is happy that she is getting married, but she is also not happy that her ex-boyfriend showed up at the wedding. She is happy about one thing and not happy about a different thing, so there is no real inconsistency. 7.1.2

Entailment

A set of statements P\...Pn entails (or implies) a statement Q if and only if Q follows logically from Pi... Pn. In other words, if Pi... Pn are all true, then Q must also be true. For example, consider these statements: P: A bomb exploded in London. Q: Something exploded somewhere. Here, P entails Q, but not the other way round. Just because there was an explosion does not mean that a bomb was involved. Perhaps it was it was an egg exploding in a microwave oven. When P entails Q, we say that Q is a logical consequence of P. In symbolic notation, it is P => Q. Here are two important points about entailment: • A set of true statements cannot have false consequences. • A set of false statements can have true consequences. If we look at the example carefully, we can see that if P entails Q, and Q turns out to be false, then we should conclude that P must also be false. This point is worth remembering because we often decide that a hypothesis or a theory is false because it entails something false. However, if P entails Q, and P is false, it does not follow that Q is also false. A false theory can have true consequences, perhaps as a lucky accident. Suppose someone believes that the Earth is shaped like a banana. This false belief entails that the Earth is not like a pyramid, which is true. This example tells us we should avoid arguments of the following kind: Your theory entails Q. Your theory is wrong. Therefore, Q must be wrong. Entailment is related to the logical strength of statements. If a statement P entails another statement Q but not the other way round, then P is stronger than

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Q, or equivalently, Q is weaker than P. Thus "That is a Boeing 747 airplane" is stronger than "That is an airplane." As you can see, a stronger statement provides more information, but at the same time it runs a higher risk of being false. Here are some typical ways to qualify a statement to make it weaker: Original statement

Weaker, qualified version

All lawyers are talkative.

All lawyers / know are talkative. (restrict to personal experience)

Snakes with triangular heads are poisonous.

Most snakes with triangular heads are poisonous. Snakes with triangular heads are probably poisonous. Snakes with triangular heads are often poisonous. With few exceptions, snakes with triangular heads are poisonous. (frequency and probability qualifiers)

He won't be late.

/ / there is no traffic jam, he won't be late. (conditional qualifier)

He is tall. This cake is good.

He is not short. This cake is not bad. (weaker adjectival phrase)

Although qualifying a statement might make it more plausible, do not overdo it. "The government should increase taxes now" makes a definite and substantive claim. "The government should increase taxes when it is appropriate to do so" is so weak as to say nothing. Highly qualified writing can appear to be boring and wishy-washy. A well-argued but interesting claim is much preferable. We should also be careful of the opposite situation in which people fail to qualify their claims for various reasons. For example, some people believe shark cartilage can cure cancer, and there is even a book called Sharks Don't Get Cancer. But it turns out that sharks do get cancer. The book does acknowledge that, but it says that a qualified claim such as "almost no sharks get cancer" would not make a good book title. Guess what, sharks can even get cancers in their cartilage! 7.1.3

Logical Equivalence

If P entails Q and Q entails P, then P and Q are logically equivalent—for example, "Superman is more powerful than Batman" is logically equivalent to "Batman is less powerful than Superman." When two statements are logically equivalent, they necessarily have the same truth value—it is not possible for one of them to be true and the other one to be false. • In formal logic, P o Q means that P and Q are logically equivalent. • If P o Q, then Q o P. Every statement is logically equivalent to itself.

LOGICAL CONNECTIVES

7.2

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LOGICAL CONNECTIVES

A logical connective is a logical term that can be attached to statements to form more complex statements. 7.2.1

Conjunction

Given two statements P and Q, their conjunction is the complex statement "P and Q". P is the left conjunct, Q the right conjunct. Examples: • Jack died, and Jill went to a party. • Protons are positively charged, and electrons are negatively charged. The logical behavior of a conjunction is quite simple. A conjunction "P and Q" is true when both conjuncts P, Q are true. Otherwise the conjunction is false. But be careful of possible ambiguity when and is used to join phrases: • Ravel studied the philosophy of music and literature. (Literature and philosophy of music, or philosophy of music together with philosophy of literature?) • We should hire more temporary and part-time drivers. (Temporary drivers and part-time drivers, or part-time drivers who work on a temporary basis?) • You must use screws, nuts, and bolts of stainless steel. (Are the screws and nuts also made of stainless steel?) 7.2.2

Disjunction

Disjunction is expressed by the word or in English, but it is useful to bear in mind two types of disjunction. When "P or Q" is used in the exclusive sense, this is equivalent to "either P or Q, but not both." An example might be when a girl issues an ultimatum to her two-timing boyfriend: "Either you stay with me, or you go out with her." Presumably she is not saying that her boyfriend can do both! On the other hand, under the inclusive reading, "P or Q" is consistent with the possibility where both P and Q obtains. Suppose your computer is not working, and your friend says, "The hard drive is broken or the motherboard is not working." We might not want to say that your friend is wrong if it turns out that both components are not working. The two possible interpretations presents a potential problem in drafting and interpreting legal documents. 1 To avoid disputes and unintended consequences, it might be a good idea to be more explicit when disjunction is used, by adding 1 Some linguists and philosophers argue that or has only the inclusive meaning. Any impression otherwise is due to conversational implicatures or other pragmatic effects. Whatever the case may be, there is no harm in making things clearer when we want to avoid misunderstanding.

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"or both", or "but not both." Also, like and, the use of or can lead to syntactic ambiguity: • You should use white glue or tape. (Does the tape have to be white?) • No hunting of turtles, fish, or birds on the endangered list. (All turtles and fish, or just those on the list?) 7.2.3

Negation

The negation of a statement P is any statement whose truth-value is the opposite of P. Given any statement in English, we can form its negation by appending the expression "it is not the case that." So the negation of "it is raining" is "it is not the case that it is raining," or, in other words, "it is not raining." Here are some facts about negation: • A statement and its negation are always inconsistent with each other. • A statement and its negation form a pair of exhaustive and exclusive alternatives, e.g. Santa Claus exists; Santa Claus does not exist. They cannot both be true and they cannot both be false.2 • Negation involving modal verbs in English can be tricky. "You must leave" and "you must not leave" are inconsistent. But they are not exhaustive alternatives because it is also possible that there is nothing you must do. Perhaps it is up to you whether you stay or leave. The negation of "you must leave" is "it is not the case that you must leave," not "you must not leave." However, the negation of "you may leave" is "you may not leave"! • In formal logic, the negation of P can be symbolized as ~P, ->P, or not-P. 7.2.4

The conditional

A conditional statement (or a conditional) is any statement of the form "If P then Q"—for example, "If you are a member, then you can get a discount." Conditionals are of special importance because they can be used to formulate rules and general laws: • Computer programs contain lots of rules about what to do in some given situation. A rule for removing spam messages might be: "If an email contains the words viagra and sex, put it in the trash folder." • Many universal scientific laws are conditionals in disguise. "All electrons have negative charge" is equivalent to "For any object x, if A: is an electron, then x has negative charge." 2

Recall Section 4.6 on exclusive and exhaustive possibilities.

LOGICAL CONNECTIVES

65

• A lot of legal rules are conditionals describing the legal consequences of specific situations—for example, if you are in a moving vehicle equipped with seat-belts, then you are required to wear one. Given a conditional "if P then Q", P is the antecedent of the conditional, and Q the consequent. To accept a conditional is to accept a certain logical or evidential connection between P and Q. But you don't have to accept that P and Q are both true. For example, you might agree with this statement: If the sun explodes tomorrow, then we shall all die a sudden death. But you can consistently agree that the statement is true, even if you do not believe that the sun will explode tomorrow, and you also do not believe that we shall all die suddenly. Here are some additional points about the conditional: • These claims are correct: - When P is true but Q is false, "If P then Q" is false. "If you drink coffee you won't be able to sleep" is false when you still manage to sleep after drinking coffee. - "If P then Q" is logically equivalent to "If not-Q, then not-P". - P. IfP then Q.=>Q. - Not-Q. If P then Q. => not-P. • But please note that the two claims below are false: - Not-P. If P then Q. => not-Q. - Q. If P then Q. => P. • The converse of "If P then Q" is "If Q then P". (In other words, the antecedent and the consequent are swapped.) Normally, a conditional does not entail its converse.3 7.2.5

The biconditional

A biconditional is any statement of the form "P if and only if Q". This is logically equivalent to: If P, then Q, and if Q, then P. In other words, a biconditional is a conjunction of a conditional and its converse. Here are some equivalent formulations:

3

Unless for conditionals such as "If P then P"\

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BASIC LOGIC

• PiffQ. • P when and only when Q. • P «— Q (in formal logic) Here is a more technical point that you might skip if you want: P «- Q is not the same as P o Q. If P o Q is true, then P

correct

■

I\

Libby is a dog.

Libby is genetically cloned from a dog.

I wrong

IIP

"Libby is a terrier" and "Every terrier is a dog" are co-premises, because both are necessary to support the conclusion "Libby is a dog." If Libby is not a terrier, the mere fact that every terrier is a dog offers no reason to think that Libby is a dog, since Libby could be a cat. Similarly, if for some reason not all terriers are dogs, the fact that Libby is a terrier will not support the conclusion that Libby is a dog. This is why the two premises work together to support the conclusion. On the other hand, the premise "Libby is genetically cloned from a dog" is an independent premise. Even if Libby is not a clone, this does not affect the degree to which the other two premises support the conclusion. The third premise is therefore not a co-premise with the first two. It is a good idea in argument analysis to distinguish between co-premises and independent premises. Co-premises that work together form a single argument, whereas independent premises do not. This helps us count the number of arguments we have for a conclusion. In argument mapping, arrows leading from co-premises in a single argument are joined together before pointing to their con-

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ARGUMENT MAPPING

elusion. Separate arrows are used for other independent premises so that distinct arguments are not mixed together. Try to follow this convention in drawing argument maps because it represents more accurately the logical structure of arguments, especially when you have a single argument map that includes both copremises and independent premises, as in the diagram above. In other situations, if the argument map does not involve both co-premises and independent premises, it might not matter whether you use distinct arrows or a single arrow joining all the premises. So both versions are fine in the following maps, even though strictly speaking only the one on the right is correct.

Smoking Smoking Smoking makes you stains your causes smell. teeth. cancer.

I

I

You should not smoke.

11.2.5

I

Smoking Smoking Smoking makes you stains your causes smell. teeth. cancer.

1

r- You should not smoke.

correct

Make hidden assumptions fully explicit if possible

When people give arguments sometimes certain assumptions are left implicit. Here is a popular argument against homosexuality: Homosexuality is morally wrong because it is unnatural. To evaluate this argument, apply the fourfold path discussed in the beginning of this book and start with the question "What does it mean?" In particular, what does the word unnatural mean in this argument? If unnatural means "does not occur in the natural environment", then it is not so clear that homosexuality is unnatural, since biologists have observed homosexual behavior in over a thousand species of animals. The next question to ask is, "Is it reasonable?" and we can see that this argument is invalid. Even if homosexuality is unnatural, it does not follow that it is wrong. The conclusion might be thought to follow if it is assumed that whatever that is unnatural is wrong. Adding this premise will make the argument valid. But is the new premise true? Surely there are lots of "unnatural" things that are not wrong, such as video games, brain surgery, and sunglasses. If these things are not objectionable, why is homosexuality any different? Revealing hidden assumptions is an important part of argument analysis. Many people are busy, sloppy, and sneaky, and many arguments presuppose assumptions that are not made fully explicit. One way to discover these assumptions is to check whether premises have to be added to make an argument valid. This will be easier if we are familiar with typical patterns of valid and invalid arguments.

SOME NICETIES

101

Another method that is particularly useful in argument mapping is to follow these two guidelines:1 • The holding hands rule: Every key term appearing in a premise of an argument but not in the conclusion must also appear in some other premise. • The rabbit rule: Every key term appearing in the conclusion of an argument must also appear in at least one of the premises. These two rules are only guidelines because they have exceptions, but they are still very useful in formulating arguments for which the reasoning from the premises to the conclusion is made explicit. They are particularly useful in drawing argument maps, and looking at an example will help us better understand how they work and their rationale. Let us return to the last argument:

Homosexuality is unnatural.

I

Homosexuality is morally wrong.

The underlined phrases show that the argument violates both the rabbit rule and the holding hands rule. The rabbit rule is violated because the concept of something being morally wrong appears in the conclusion, but it cannot be found anywhere in the premises. The motivation for the rabbit rule is to ensure that different parts of the conclusion can be traced back to the premises. In general, if a concept is present in the conclusion, some assumption must have been made relating to the concept in question. The aim of the rabbit rule is to make these assumptions explicit and show how the premises lead to the specific conclusion. Otherwise it might not be clear how the conclusion comes about. When the conclusion suddenly introduces something that has not been mentioned before, it is like a magic trick, producing a rabbit out of a magician's hat! On the other hand, the word unnatural is underlined to show that the holding hands rule has been violated. The rationale for this rule is to ensure relevance. If a concept appears in a premise but not the conclusion, we might wonder why that concept is mentioned at all. What work does it actually do in the argument? Is it really necessary? By requiring that the concept appears again in another premise, we hope to ensure that the premises are linked together ("holding hands") in a way that reveals the role of the concept in the reasoning process. Returning to our example, consider the following modified argument map: 1

The rules camefroma set of argument-mapping tutorialsfromthe Australian company Austhink.

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ARGUMENT MAPPING

Homosexuality is unnatural.

Anything that is unnatural is morally wrong.

I

T

Homosexuality is morally wrong. The underlined phrases in the argument now come in pairs, indicating that when the hidden assumption has been added, the argument map satisfies both the rabbit rule and the holding hands rule. When the rules are followed, the reasoning of the argument is clearer. But there are a few points to note. The rabbit rule and the holding hands rule are only guidelines. They are not to be applied mechanically without exception. First, we should not apply them to logical words like if... then ..., every, nothing, some, and any. These words are not specifically about a particular subject matter, unlike words such as recession, dolphins, and morally wrong. So even though the word anything still violates the holding hands rule in the argument map above, this is perfectly fine. Furthermore, an argument that satisfies the two rules might still be a bad argument. The rules help us improve the clarity of arguments. But a clear argument can still contain bad reasoning and false premises. So bear this in mind when you evaluate an argument. 11.2.6

Dealing with objections to reasoning

It is a bit tricky to use argument maps to display objections to reasoning rather than the truth of premises. Consider this argument: All fish have gills. Dolphins are not fish. So dolphins do not have gills. The argument satisfies both the rabbit rule and the holding hands rule, and the premises and the conclusion are true. But the reasoning is problematic. This might be indicated on an argument map as follows:

All fish have gills.

Dolphins are not fish.

I

■ OBJECTION

Conclusion does not follow.

Dolphins do no have gills. There are certainly other possibilities. Someone who offers such an argument probably mistakenly assumes that if all fish have gills, it follows that if something

EXERCISES

103

is not a fish, it does not have gills. This is of course a mistake since creatures other than fish might also have gills. We can include this inference into an argument map, and object to this intermediate conclusion:

M fish Conclusion should be: have gills. If something does not { have gills, it is not a fish. I f s o m e t h i n g is _'„._.T not a fish, it does OBJECTION ►- not have gills.

'

Dolphins are not fish. v i

Ï

'

Dolphins do no have gills. As you can see, there are different ways of representing objections to reasoning using argument maps. There is no standard notation so you can use your own as long as it is easy to understand. EXERCISES 11.1 Simplify and rewrite these arguments in the standard format and fill in any missing premises. a) Gold is a metal. Therefore it conducts electricity. b) God does not exist. So life is meaningless. c) Noam is a thinker. So he is not a doer. d) Biden is heavier than Obama. Fatima cannot lift Obama. So there is no way she can lift Biden. e) The whole building collapsed. So probably many people died. f) Anyone who donates $1000 will become a member. John is a member. So he must have donated $1000. g) I certainly had fruit today. Ketchup is made of tomatoes, and nobody can deny that tomatoes are fruits. h) We should impose the death penalty on people who sell or possess illegal drugs because this is going to eliminate the majority of criminal activities. 11.2 Draw argument maps for these arguments. No need to fill in the hidden premises. a) Johnny is sick. He should not go to school. b) The road is dangerous. It is slippery because there was an oil spill. Also, there is no electricity so the lights are out. 11.3 Draw argument maps for the passages below. Fill in the more important hidden premises and conclusions. Distinguish between independent premises and co-premises where feasible.

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ARGUMENT MAPPING

a) High school students should learn subjects that improve their critical thinking. Philosophy does just that. Philosophy is also fun. b) Tourism benefits the economy. Improving the environment will attract more tourists. Besides, a better environment improves the quality of life for everyone. 11.4 Correct these argument maps. Distinguish between independent premises and co-premises. Fill in missing premises by applying the rabbit rule and the holding hands rule. Adjust the arrows if needed. There is no need to evaluate the argument, so do not worry about false premises. a) Every human is mortal Socrates is mortal b) Whenever it rains, there will be a traffic jam

He will be late

c)

OBJECTION

Some dinosaurs are warmblooded

All warmblooded animals are mammals

X

REASON

Whales are warmblooded

Whales are fish

REASON

Whales are mammals *■

OBJECTION

11.5 Draw an argument map with only these sentences as premises and conclusions. The last sentence is the main conclusion. 1. Either Dumbledore and Harry are playing quidditch or Harry and Hermione are studying in the library. 2. If Dumbledore and Harry are playing quidditch, then Harry will win the game. 3. If Harry and Hermione are studying in the library, then Hermione is studying in the library. 4. If Hermione is cooking, then she is not studying. 5. If Hermione is not studying, then she is not studying in the library. 6. If Hermione is cooking, then she is not studying in the library. 7. Hermione is cooking. 8. Hermione is not studying in the library. 9. It is not true that Harry and Hermione are studying in the library.

EXERCISES

105

10. Dumbledore and Harry are playing quidditch. 11. Harry will win the game. 11.6 Kl Consider the claims below. Do some research about them and draw an argument map showing the arguments for and against each claim. a) The world should rely more on nuclear power. b) Torture should not be made legal. c) The police should not use entrapment to catch criminals. d) God exists.

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CHAPTER 12

ARGUMENT ANALYSIS

12.1

WHAT IS A GOOD ARGUMENT?

We have discussed different aspects of arguments. It is time to consider how they help us explain what a good argument is. Intuitively, a good argument is one in which the premises provide good reasons for the conclusion. This is of course quite vague. Let us try to make it more precise. Condition 1 : The premises are true or highly plausible The premises of a good argument must be known to be true, or they have to be at least highly probable. This criterion should be rather obvious. We have no reason to accept an argument if the premises are false or are unlikely to be true. Condition 2: The argument is deductively valid or inductively strong Deductively valid arguments are of course valuable. Valid arguments cannot lead us from true premises to false conclusions. But we have seen that inductively strong (and hence invalid) arguments play an equally important role in reasonAn Introduction to Critical Thinking and Creativity: Think More, Think Better. By Joe Y.F. Lau Copyright © 2011 John Wiley & Sons, Inc.

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ing. It will be too restrictive if we demand that all good arguments must be valid. We would have to give us most of our scientific knowledge. Note that if a good argument is either valid or inductively strong, this implies that an inductively weak argument can never be a good argument.

Condition 3: The premises are not question begging The first two conditions are still not sufficient for a good argument. Consider this circular argument, where the conclusion appears as a premise: Oatmeal is good for your health. Oatmeal is good for your health. This is surely a bad argument since no independent reason has been given to show why oatmeal is healthy. However, the argument is actually sound. First, the premise is indeed true, because oatmeal has lots of fibre and can lower blood cholesterol. Furthermore, the argument is valid. Since the premise is the same as the conclusion, it is impossible for the conclusion to be false when the premise is true! This example shows that not all sound arguments are good argument. To deal with this problem, we should require that the premises of a good argument cannot be question-begging—that is, they should not assume what the argument is trying to establish. (See also page 176 for further discussion.)

Condition 4: The premises are all relevant to the conclusion Consider this argument: Albert Einstein was a physicist. All physicists studied mathematics. Albert Einstein played the violin. Albert Einstein studied mathematics. This is presumably a non-question-begging, sound argument. If we accept the premises, we ought to accept the conclusion. Yet there is something wrong with the argument—namely, that the third premise is irrelevant to the conclusion, even though it is true. If we remove this particular premise, it does not affect the strength of the argument at all. The extra premise is a distraction and liable to create confusion, and it fails to provide a good reason for the conclusion. Bearing this in mind, we should require that a good argument does not contain any irrelevant premises.

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109

Summary: Definition of a good argument 1. The premises are true or highly plausible. 2. The argument is deductively valid or inductively strong. 3. The premises are not question-begging. 4. All the premises are relevant to the conclusion.

12.2

FOUR WAYS TO ATTACK AN ARGUMENT

Now that we know what a good argument is, what should we do when we come across an argument that is nor good? It is important not to rely on your gut feeling and just dismiss the argument. See if you can think of one or more reasons why the argument should be rejected. In general, there are four main ways to attack an argument: two direct methods and two indirect ones: 1. Direct method 1: Attack the premises. If you can show that an argument relies on at least one implausible premise, that is a good way of showing that the argument is not good enough. But sometimes you do not have to go all the way to show that a premise is false. You might argue that there is simply not enough evidence to show that the premise is true. This falls short of arguing that the premise is false, but it passes the burden of proof to the opponent. But remember, just because an argument has a false premise, it does not follow that the conclusion is false! 2. Direct method 2: Attack the reasoning. Even if the premises are all very plausible, you need to check whether the reasoning of the argument is acceptable. The argument might be invalid or inductively weak, or question begging. 3. Indirect method 1: Attack the argument indirectly by attacking the conclusion. If you can show that the conclusion of an argument is false, this implies that there must be something wrong with the argument. This strategy of refuting an argument is useful when it is difficult to evaluate an argument directly, perhaps because it is too long or convoluted. Of course, this strategy does not really explain what is wrong with the argument. 4. Indirect method 2: Give an analogous argument that is obviously bad. The idea is to compare the original argument with another argument. If the new argument is obviously bad, and it has the same structure as the original one, then the original one is likely to be a bad argument as well. This is a good strategy to use when it is difficult to see what is wrong with an argument, or your opponent refuses to admit that the argument is no good.

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ARGUMENT ANALYSIS

As an example, consider this argument: Capital punishment is wrong because it is always possible to punish an innocent person by mistake. We might attack the argument using the four methods as follows: • Attack the premises: Is it always possible that an innocent person is executed by mistake? It might be argued that in some crimes there were many independent witnesses. Perhaps the criminal was apprehended right away at the crime scene, and the whole crime was recorded on surveillance video. There is therefore little doubt that the person being caught is guilty. • Attack the reasoning: Even if mistakes are always possible, this is just one consideration and it does not immediately follow that capital punishment is wrong. Maybe there are many other considerations in support of capital punishment. We need to balance these factors before deciding whether capital punishment is acceptable or not. • Attack the conclusion: Punishment should be proportional to the crime. Capital punishment is not wrong because this is what justice requires in the case of hideous crimes. • Give an analogous argument that is obviously bad: With imprisonment, it is also possible to punish an innocent person by mistake. But it would be absurd to stop sending people to jail because of this. Of course, there is a lot more we can say about capital punishment. The responses just given might not be very convincing, and you need not agree with any of them. They serve only to illustrate the fact that many arguments can be attacked in more than one way. 12.3 ARGUMENT ANALYSIS: CHECKLIST The analysis of argument is one of the most basic parts of critical thinking. To sum up, there are three main steps: 1. Clarify the argument. 2. Evaluate the argument. 3. Think about further relevant issues. We have already discussed many aspects of this process. The table below lists some of the main tasks involved. You can use this as a checklist when you want to analyze an argument systematically. It would be good to internalize these steps as part of your natural thinking habit:

EXERCISES

Step

Tasks and questions

1. Clarify the argument

Identify premises and conclusion. Clarify the keywords. Simplify the argument using your own words. Draw an argument map.

2. Evaluate the argument

Is the argument a good one? Are the premises plausible? Is the argument valid or inductively strong? Any fallacy in the argument? (See Chapter 19.) Any reason to think that the conclusion is false? Any obvious counterexample?

3. Explore further issues

How good is the argument overall? How important is the argument? Is the conclusion surprising? Can the argument be repaired or improved? Are there other arguments with similar conclusions? What about arguments with the opposite conclusion? Can the argument be applied elsewhere? Any further information that might be relevant?

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EXERCISES 12.1

Are these statements true or false? a) Not all sound arguments are good arguments. b) Some inductively strong arguments are not good arguments. c) If a good argument is invalid, it also cannot be inductively weak. d) A good argument that is not inductively strong must be valid. e) A sound argument can contain irrelevant premises. f) If an argument is inductively weak, it cannot be a good argument. g) If an argument is not good, it is either inductively weak or unsound.

12.2

Which of these arguments are question begging? a) I like anything that is sweet. Chocolate ice cream is sweet. So I like chocolate ice cream. b) I like chocolate ice cream because chocolate ice cream is what I like. c) I like chocolate ice cream best, because it is my favorite ice cream. d) I ordered chocolate ice cream, because it is my favorite ice cream, and I always order my favorite ice cream.

12.3

Apply the direct and indirect methods to criticize these arguments: a) Cloning animals or human beings is unnatural, so it is wrong and we should not do it.

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ARGUMENT ANALYSIS

b) We should not trust scientists because they keep on changing their theories. Today they say that this is true. Tomorrow they come up with a different theory and say something else. c) It is useless to punish students because they will always make mistakes. 12.4 Evaluate these arguments and in particular pay attention to any hidden assumptions. a) Low taxation is desirable because it has lots of benefits. It is good for business and investment, and the citizens are likely to be happier. b) The universe could not have existed forever. Radioactive material will decay until they cease to become radioactive. Since the universe still contains radioactive material, there must have been a beginning. Otherwise all the radioactive material will have long been gone already. c) Indira donated $2 million to the Democratic Party and only $500,000 to the Liberal Party. So she is probably going to vote for the Democratic Party.

CHAPTER 13

SCIENTIFIC REASONING

Science is regarded as one of the greatest achievements of human beings, alongside art, music, and literature. Technology is a product of science, and it has a huge impact on our lives. But the core of scientific methodology is hypothesis testing, an essential part of critical thinking. Broadly speaking, hypothesis testing is a matter of gathering evidence to select the best hypothesis. (In this book, a hypothesis is the same as a theory or a claim— a statement that can be either true or false.) But hypothesis testing is not just for scientists. In any type of career, we have to solve problems, and hypothesis testing helps us find the best solutions to our problems. Suppose your mobile phone is not working. Is the battery dead or is the phone broken? You try to recharge it to see if it works. If it does the phone wasn't broken. This is hypothesis testing. Or think about how to improve your health. What should you eat and what exercises should you do? You need to gather information and evaluate different theories before coming up with a plan. This also involves hypothesis testing. There are two noteworthy features about hypothesis testing. First, it is based on evidence, not on gut feelings, tradition, popularity, authority, or personal preferences. Second, hypothesis testing is fallible, and it is often difficult to prove that a theory must be correct. Our evidence might be tainted without our knowledge, An Introduction to Critical Thinking and Creativity: Think More, Think Better. By Joe Y.F. Lau Copyright © 2011 John Wiley & Sons, Inc.

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SCIENTIFIC REASONING

or perhaps the evidence is inconclusive. This does not mean we should give up scientific reasoning. We do our best to identify the theory that has the highest probability. It is too bad if we turn out to be wrong, but such is the uncertainty of life. This is like investing in the stock market. Nobody can predict the future accurately all the time. But someone who is correct 70% of the time will already be doing very well.

Scientific reasoning and investment George Soros is one the world's wealthiest hedge fund managers. In 1992, he famously traded against the Bank of England. He won and made a huge profit, and Britain was forced to give up its fixed exchange rate. Soros attributed a large part of his investment successes to the use of scientific reasoning. Before he makes a trade he formulates a hypothesis about what is happening in the market. He then tests his hypothesis, and if the market goes against it he immediately cuts his losses. He gives this advice about making reliable investment decisions: Talk to people who have the opposite view, and see if you change your mind afterward. This is a good piece of advice to combat confirmation bias (We discuss confirmation bias on page 189).

13.1 THE DEAR METHOD We now look at the four main steps in hypothesis testing. We call this the DEAR method, which reminds us of the first letter of the keyword in each of the four steps. 1. Define the hypothesis to be tested. 2. Collect the evidence for and against the hypothesis. 3. List all the alternative hypotheses. 4. Rank them and pick the best one to accept. Where do these hypotheses come from in the first place? The answer is that they can come from anywhere. They might arise from the problems that we are trying to solve or from observations that we have made. For example, we might have seen lots of white swans and so we wonder whether it is true that all swans are white. However, what makes a hypothesis scientific is not how it comes about. A scientific hypothesis is a clearly specified statement that can be tested in principle. Many scientific theories have been inspired by dreams or wild speculations. They can still be acceptable if we have good evidence showing that they are true.

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115

13.1.1 Step 1 : Define the theory to be tested The first step of hypothesis testing is to define clearly the hypothesis that is to be evaluated and make sure we know what it means. If the meaning of a hypothesis is unclear, it will be difficult if not impossible to test it. Here are a few things to bear in mind: • Clarify keywords: Some people think that everyone is surrounded by an aura field, a field of energy. To test this hypothesis, we need an explanation of what an aura energy field is. Is it the same as the electromagnetic energy that is studied in physics? If so then there are ways to test its presence. In fact this is probably true since our bodies have warmth and so they emit heat, which is a form of electromagnetic energy. But then the aura field is not something very remarkable. On the other hand, if this is not what is meant by an aura field, then further clarification is needed. Otherwise there is no way to test the hypothesis and we have no reason to believe it. We might as well say there is an invisible and undetectable unicorn dancing on everyone's head. • Be precise: A more precise hypothesis is less likely to be misunderstood. Take the claim that gold is a good investment. Its meaning is not obscure, but more precision will provide better guidance. Are we supposed to buy real physical gold, or stocks that are linked to gold? Is this good investment for the short or long term? What kind of return are we talking about? Taking these concerns into account might give us a more concrete claim, such as investment in physical gold or gold stocks will beat inflation and perform better than major stock markets in the next five years. • Clarify the scope of the hypothesis: The scope of a claim is the range of things the claim is supposed to be true of. Take the claim "swans are white." Is this true of all swans, most of them, or just some of them? The scope of the claim makes a big difference as to the evidence we need to check whether the claim is true. "All swans are white" is false because there are black swans in Australia. But if the claim is changed to "some swans are white," the existence of black swans becomes irrelevant and what matters is whether you can find at least a few white swans. But consider also "most swans are white." Knowing that there are white swans and black ones will not help us decide whether it is true. We need a detailed statistical survey to find out. As you can see, the scope of a theory makes a big difference to the evidence needed to test it.

13.1.2 Step 2: Gather the evidence for and against the theory To evaluate a hypothesis, we gather all relevant evidence. • There are two types of evidence: Supporting evidence are facts that increase our confidence in a hypothesis. Counterevidence are facts that de-

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SCIENTIFIC REASONING

crease our confidence. Generally speaking, a piece of supporting evidence provides a reason for thinking that the hypothesis is true. This happens when some fact obtains which is what we should expect given the hypothesis. Counterevidence is the opposite. For example, the hypothesis that all swans are white implies that the next swan we see will be white. So if we do see a white swan, that counts as supporting evidence, and if we see a black swan, that would be counterevidence. Or take a different example. There being lots of dark clouds is supporting evidence for the hypothesis that it will rain soon. If the air pressure is low, that is another piece of supporting evidence. But a bright and clear sky will be counterevidence instead. What if it is a windy day? This is neither supporting evidence nor counterevidence since wind makes no difference to the likelihood of rain. • Evidence can differ in strength: Seeing a single white swan is weak supporting evidence that all swans are white. Finding lots of white swans in different countries would be much stronger evidence. But this is not conclusive evidence, evidence that proves or disprove a hypothesis beyond reasonable doubt. Unless you have seen all the swans there are, you can never be sure that they are all white. On the other hand, seeing a single black swan does count as conclusive counterevidence against the hypothesis that all swans are white. So when we gather evidence we have to decide two things: first, whether it is supporting evidence or counterevidence, and second, whether the evidence is weak, strong or conclusive. The assessment of the evidence will affect our confidence in the hypothesis. • The more evidence the better: Finding more evidence in support of a hypothesis means we can be more confident that it is true. So avoid relying on a single piece of evidence. But remember that a hypothesis can be wrong even if we have lots of supporting evidence that is not conclusive. Furthermore, human beings are prone to pay more attention to evidence that agrees with their own opinions. So if you agree with a hypothesis, make a special effort to come up with counterexamples, and seek out people who disagree with you to see if they know of counterevidence that you do not.

13.1.3 Step 3: List all the alternative theories The world is a complicated place and things are often not what they seem. When we have a theory that seems to explain the evidence, we should actively consider whether there are alternative theories that provide even better explanations. If you have a severe stomachache, it might be due to something you just ate. But it could also be acute appendicitis, which can be life threatening. An alternative theory is one that is (1) distinct from the theory you are considering and (2) broadly consistent with the evidence you have observed. For example, it is now widely acknowledged that the Earth's temperature is increasing, and this global warming is caused by pollution and other human activities. But an alternative theory to consider is that the temperature increase is only part of the natural

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fluctuation in climate. Sometimes the Earth gets cooler and sometimes it gets hotter. It just so happens we are in the hotter period but it has little to do with us. Sometimes we can rule out an alternative theory by getting more evidence. To decide whether global warming is due to natural climatic fluctuations, scientists look at historical records and ice core samples to measure the extent of natural temperature variation in the past and see whether this accounts for recent global warming, and the conclusion is negative—global warming is due to recent human activities. Coming up with alternative theories requires knowledge and imagination, and the truth might not be obvious. Human beings are often affected by biases, and they view the world through perspectives they are most attached to. Some people like to invoke the supernatural whenever there is something that is puzzling— for example, a butterfly refused to fly away after Daddy passed away so it must have been his reincarnation. Others like to resort to divine command, such as it is God's will. Still others like to blame things on their favorite target, saying it is the fault of the government / the society / my teacher / my parents / my girlfriend, and so on. Good scientific reasoning requires us to actively challenge our default explanation. This is not just a matter of being open-minded. We need the courage to accept that our most favorite or most comfortable point of view might not be the correct one. 13.1.4

Step 4: Rank the theories and pick the best one

Once we have come up with a list of alternative theories, we can evaluate them carefully and pick the one that is most plausible. This method of reasoning is known as inference to the best explanation, which is of the following form: We have a set of evidence E. X,Y,Z,... are all theories compatible with E. X provides the best explanation of E. X is most likely to be true. But how do we find out which theory provides the best explanation? The answer is that we need to appeal to more general theoretical considerations: 13.1.5

Predictive power

Predictive power is about the quantity and quality of the predictions made by a theory. Quantity is about the number of predictions that can be made. A theory that generates no prediction at all fails the minimal requirement for a scientific hypothesis. A claim that cannot be tested can perhaps still be meaningful. It might even be true. But if we believe the claim, it only can be a matter of faith and not reason since there is absolutely no evidence to justify the belief. The quality of prediction is about precision and accuracy. If an astrologist predicts that an old man is going to die within 20 years on the basis of the position of

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the planets, and the man dies 10 years later, this is not too impressive. But suppose the astrologist predicts that the man will be crushed to death by a jet engine falling from the sky exactly 20 years and one day later. If the prediction turns out to be right, this would be a very impressive accomplishment. A few more of such correct predictions, we might even become believers of astrology! When the predictions of a theory turn out to be wrong, it is possible to save the theory by challenging some of the auxiliary assumptions. These are assumptions we make about the theory or about the experimental setting that helps us generate the prediction. For example, to test the hypothesis that water freezes at 0°C, we can use a thermometer to measure the temperature of ice, but the auxiliary assumption here is that the thermometer is accurate. When a theory fails to be confirmed by evidence, one way to save the theory is to reject some of these auxiliary assumptions. For example, some people claim they have telepathic abilities that enable them to read other people's minds. When being tested repeatedly in an experimental setting, they inevitably fail to perform better than others who are simply guessing. A frequent response of the defenders of telepathy is to challenge the auxiliary assumption that the experimental setting will not interfere with telepathic activities. They might say that the scientists carrying out the experiments have hostile and negative thoughts that interfere with the concentration and abilities of these practitioners. This justification (or excuse) is called an ad hoc hypothesis, one that is introduced solely to avoid disconfirmation of a theory. It is of course legitimate to question auxiliary assumptions when a hypothesis has been disconfirmed. But the challenge should be motivated by good reasons. A secondary school student repeating a well-known scientific experiment might obtain results contrary to expectation. But this is probably because there is something wrong with the setup and not because a well-established theory has been proven wrong. Introducing ad hoc hypotheses need not be objectionable since they could turn out to be true. What is objectionable is to save a theory from refutation by introducing ad hoc hypotheses one after another, without making a serious attempt to find concrete and rigorous ways to test the theory. 13.1.6

Mechanism

Sometimes two events can be correlated without there being a direct causal link between them. There might be a positive correlation between ice cream sales and the number of shark attacks in Australia, but it does not mean selling more ice cream causes sharks to attack human beings. This correlation might seem strange until we note that shark attacks happen more often in the summer when more people eat ice cream. This underlying explanation allows us to understand the link between the correlated events. In general, we should choose theories that explain the causal mechanisms between events. Understanding the details of the mechanisms allows us to generate more predictions to test the theory and make other discoveries. It might also help us forge connections with the rest of our scientific knowledge.

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Fruitfulness

The last point about mechanism is related to fruitfulness—whether a theory helps us make surprising or unexpected predictions that turn out to be correct and whether the theory helps us detect and explain connections that we would not have noticed otherwise. Consider the theory of plate tectonics, which says that the surface of the earth is covered by a series of plates floating on a viscous mantle and moving in relation to one another. After the theory was first developed in the 1960s, it generated a host of new predictions and explanations which were subsequently confirmed. For example, geologists were able to gain new insights as to why earthquakes tend to be concentrated along oceanic trenches and spreading ridges (because they correspond to frictional boundaries between plates), why marine animal fossils can be found on mountains thousands of meters above sea level (the plates pushed up against each other forming mountains), and why the eastern part of South America seems to fit together nicely with western Africa (they were once together but pushed apart by divergent plate movements). 13.1.8

Coherence

There are two kinds of coherence. First, a theory should be internally coherent— that is, logically consistent. It is possible that a useful theory is not fully consistent when it is first proposed. But inconsistency does tell us it is not completely true, so it should be revised and improved somehow. The other aspect of coherence is that good theories should be consistent with other well-confirmed theories and facts. If a purported discovery contradicts wellestablished theories, the default response ought to be that the discovery is mistaken. Strong evidence is needed to think otherwise. For example, people such as Uri Geller claim they can bend metal spoons with their minds. This certainly goes against commonsense and science. A simpler explanation is that magic or fraud is involved. To reject this more mundane explanation, we need to carefully test these people under stringent conditions, and nobody has managed to pass such tests so far. A lot of alternative medicine and claims about the supernatural should be treated with similar caution. Coherence is sometimes a matter of consistency with commonsense as well. This is particularly true of a lot of advertisements and scams. If something is too good to be true, it probably is. An advertisement might say if you attend a very expensive lecture, you will be taught a unique investment method that can double your money within a year. The advertisement might even be accompanied by testimonies from former students who vouch for the effectiveness of the method. But just think: a return of 100% is an absolutely amazing achievement, and if their method really works, wouldn't it be better for them to use the method themselves to make money rather than teach these classes? The same is true of advertisements promising that you can lose weight easily without having to exercise or change your diet. Or online scams in which strangers offer to deposit millions of

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dollars into your bank account. The fact that these solicitations do not disappear probably indicates that there are still many people who fall for them. 13.1.9

Simplicity

Roughly speaking, a simple theory is one with fewer assumptions and that posits fewer entities than its competitors. Many scientists believe strongly that we should search for simple theories if feasible. Albert Einstein once said, "Nature is the realization of the simplest that is mathematically conceivable." But why should we prefer simple theories? Is there any reason for thinking that the world is more likely to be simple than complicated? The value of simplicity as a theoretical virtue is disputed by many, and it would be impossible to settle the debate here. However, simple theories have a number of advantages. First, they are often easier to apply, so there is a practical reason to prefer a simpler theory. Second, a complicated theory postulating lots of different entities would require more evidence to support it. Finally, looking for simple theories coincide with the search for unifying causal mechanisms in our explanations. They help us understand the connections between different areas and offer a deeper explanation of the world. Weeping statues and miracles There are frequent reports of miracles by which religious statues wept tears or blood. People would come and worship the statutes and some even have claimed that the statues cured their illnesses. For example, in 2002, a Virgin Mary statue near Perth, Australia, wept red tears for nearly five months, attracting lots of pilgrims. It is of course logically possible that a miracle had occurred, but the alternative explanation is that the tears were the result of either a hoax or natural causes (such as rust or melting paint). It is interesting that the tears in this particular case were found to be a mixture of vegetable oil and rose oil. When the statute was removed and placed under observation so that nobody could tamper with it, the tears stopped. The vegetable and rose oil could of course still be a miracle. But if we apply the inference to the best explanation, taking into account considerations such as simplicity and coherence, the supernatural explanation is not the most plausible one.

13.2

RELYING ON EXPERT OPINION

We cannot possibly know everything, and inevitably we need to rely on other people's analyses and opinions, especially when it comes to scientific or technical matters. But deferring to an expert does not mean we can stop thinking criti-

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cally. In particular, we should check whether the expert is credible, accurate, and unbiased. Here is a checklist of questions to think about: • What exactly is the expert's opinion? Sometimes media headlines can misrepresent an expert's opinion. A scientist might say there is some weak evidence suggesting a correlation between A and B, but the headline might simply say "A causes B." So check the actual evidence carefully. • Is the expert in the right field? Information is more reliable when it comes from an expert who knows the topic well. In 2008, Europe's CERN laboratory was about to activate a giant particle collider for studying subatomic physics. But according to German chemist Otto Rössler, the experiment should not proceed because it might create mini blackholes that could destroy the Earth. Rössler might be an expert in chemistry, but it does not mean he is equally an expert in particle physics. The collider is now in use and luckily we are still here. • Is the expert reliable? Does he or she have a good reputation? Sometimes the expert is anonymous, so we cannot verify the reliability of the expert. So be careful with information from web pages and blog posts with no citation. Furthermore, doctorate degrees and special titles might not mean much. Even experts can often get things wrong, so it will be useful to know the past record of their opinion. • What is the context in which the opinion is made? We have seen that quotes can be taken out of context. And sometimes people are joking, being emotional, or not being serious for some other reason. An opinion expressed informally might be more of a hunch than a judgment made in a public forum. An opinion expressed by an official and reputable professional organization is more weighty than one from an unknown scientist. A study published in a well-known journal probably has gone through a more rigorous review process than an unpublished report. • Do other authorities in the same field agree with the opinion? We should be cautious if authoritative experts disagree with each other. The credibility of an opinion increases when it is free from any serious dispute among independent experts in the same area. This is one reason why it is a good idea to get a second opinion when you are deciding what to do with a serious medical condition. Of course, with about seven billion people in the world, you can expect disagreement on just about every issue. We would need to evaluate the extent of the disagreement and the arguments on both sides. • Is there any conflict of interest? If a tobacco company says smoking is healthy, the claim does not have a lot of credibility since the company would benefit from lying. Similarly, if a software company commissions an expert who then publishes a report saying that the company's operating system is the most secure one in the market, we should be somewhat skeptical of the

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report. However, it does not mean we should totally discount an opinion totally whenever a vested interest is involved. We need to consider each case individually. First, we should evaluate the evidence given for the opinion carefully and see if independent experts agree. Second, sometimes people also have a vested interest in telling the truth because they might lose more in the long run when being caught lying. • Is there any other source of bias? An opinion can be biased even if the person making the opinion does not stand to gain any material benefit. For example, if someone knows a person involved in a dispute, the relationship might affect his judgment as to who is right or wrong in the dispute. Objectivity can also be affected when someone is being emotional or in a heated discussion. Sometimes academics align themselves with a particular school of thought, and they might be dismissive of alternative perspectives. This can also be a source of bias that affects their reliability. It should be pointed out that these criteria for evaluating credibility are supposed to be general guidelines and not absolute laws. Take for example the principle that a credible opinion should be free from disagreement. This is not meant to suggest that the majority is always right. Many scientific revolutions come about precisely because certainly individuals insist on their own beliefs. It has also been suggested that those who follow the majority in the stock market are most likely to be losers in the long run and that the real winners are independent thinkers who often hold contrary opinions. However, if we insist on accepting an opinion even though some of these guidelines are violated, it must be because we have very good independent reasons for thinking that the opinion is correct.

Bertrand Russell's skepticism Philosopher and Nobel Laureate Bertrand Russell (1872-1970) has some sensible advice about deferring to experts (Russell, 1935): The scepticism that I advocate amounts only to this: (1) that when the experts are agreed, the opposite opinion cannot be held to be certain; (2) that when they are not agreed, no opinion can be regarded as certain by a non-expert; and (3) that when they all hold that no sufficient grounds for a positive opinion exist, the ordinary man would do well to suspend his judgment. These propositions may seem mild, yet, if accepted, they would absolutely revolutionize human life.

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EXERCISES 13.1 For each passage below, identify the main conclusion and the evidence given to support the conclusion. Read the passage carefully and see if there are hidden assumptions or further issues that should be considered, and whether there might be relevant possibilities and alternative explanations that would undermine the conclusion. a) Little Johnny went to a buffet and ate a lot. There were pancakes, fried rice, and chicken and all other kinds of goodies. Little Johnny was completely full and felt that he could eat no more. But then they started serving ice cream, and Little Johnny could not resist and ate a whole sundae. Right afterward he started having a stomachache. That ice cream sundae must have been contaminated or there was something wrong with it. b) An advertisement for children's vitamins introduces a person as "Doctor Kim" who then says she recommends the vitamins. So these vitamins must be good for children. c) With the economy going strong, many commercial websites have been created to enable people to shop online with ease. People who used to go shopping by driving can now order products from their homes, which will be sent to them by mail or through delivery companies. If this trend continues, we should start to see a significant reduction in the use of petrol. d) Crystals have healing power. A young woman who often had rashes on her face was told to wash her face using water in which an amethyst crystal has been left overnight. To test whether the crystal water is really effective, she was told to wash her face using just the water, and refrain from using any soap, cream, medication, or makeup. The woman was unhappy about not being able to use makeup, since she was fond of it, but she agreed to the experiment eventually. To her surprise, after using the crystal for three weeks, her rashes completely disappeared. e) Listening to Mozart's music is going to make your kids smarter and develop better cognitive skills. In a research published in the prestigious journal Nature, scientists compared three groups of college students who listened to 10 minutes of either (1) a Mozart sonata, (2) relaxation music, or (3) silence. The students who listened to Mozart did better than the rest in an abstract/spatial reasoning test conducted immediately afterward. The subjects did not have significant differences in terms of pulse. 13.2 The Scholastic Aptitude Test (SAT) is a test of verbal and reasoning skills, which is held more than once every year. Many (but not all) U.S. universities require applicants to take the test. It has been noted that the average test score of the candidates has declined over the years. One proposed explanation is that the candidates are performing less well because the quality of education has dropped. See if you can come up with a few alternative explanations.

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13.3 Some people claim to have a special sixth sense that enables them to see and communicate with ghosts. Since other people cannot see these ghosts, is this an untestable claim? If not, how would you test it? 13.4 A man said he has special psychic power and can affect people's minds. He asked a scientist to think of a number between 1 and 20, and then tell him what it is. The scientist said he was thinking about the number 18. The man then took off his own left shoe and his sock, and the scientist was surprised to see that the number 18 was written on the man's foot. The man explained that he wrote it beforehand and manipulated the scientist's consciousness to make him think about the number 18. The scientist found this difficult to believe but there was no way the man could have written the number down while they were talking. Assuming all these facts, how would you explain the successful prediction if it was not due to the man's psychic power? How would you test these various explanations? 13.5

Discuss and evaluate these claims about science. a) We accept lots of things in science even though they cannot be proven. That shows that faith is also an essential part of science, just like religion. It is therefore wrong to criticize a religion by saying that it has no solid proof. b) Psychology is not a science because psychologists cannot predict human behavior with 100% accuracy. c) Science uses induction. On the other hand, logic uses deduction.

13.6 Kl In testing a theory it is important to think about its consequences. Consider the biblical theory that there was a huge flood on Earth about 5,000 years ago, wiping out all animals and people except Noah, his seven family members and the animals he carried on the ark. If this were true, what consequences might we be able to observe? For example, think about what the geological data might say, and how the devastation would affect human history and archaeological records. If all humans and animals came from the survivors on the ark, what might this mean for genetic diversity and the geographical distribution of animal species?

CHAPTER 14

MILL'S METHODS

In science and everyday life, we think a lot about causes and effects. Knowledge about causation allows us to understand the world, make predictions, and change things. In this chapter and the next one we shall discuss some of the principles of causal reasoning. First we start with a set of rules known as "Mill's methods." They were formulated by the famous English philosopher John Stuart Mill (18061873), who wrote on a wide range of topics from logic and language to political philosophy. When we have an observed effect E, we can use Mill's methods to find its cause by following this procedure: 1. Identify a set of candidate causes— events or conditions that happened before E, and one of them is suspected to be the cause of E. 2. Collect information about a range of situations involving these candidate causes, and determine whether E occurred afterward in these situations. 3. Based on the information collected, use one of the five rules below to infer the cause of E. Let us now look at the five rules one by one and see how they are applied. An Introduction to Critical Thinking and Creativity: Think More, Think Better. By Joe Y.F. Lau Copyright © 2011 John Wiley & Sons, Inc.

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THE METHOD OF AGREEMENT If two or more situations leading to an effect E has only one event C in common, then C is the cause of E. Situation

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The method of agreement is the rule stated above, and the table illustrates how the rule can be applied. We want to find the cause of E, which was present in three situations corresponding to the three rows of the table. A, B, and C are the candidate causes that preceded E. The ticks in the first row indicate that in situation #1, A and C were followed by E. Because B did not occur in that situation, the method of agreement rules out B as the cause of E. The second situation rules out A. C is the only candidate cause common to all three situations. Applying the method of agreement, the conclusion is that C caused E. To give a more concrete example, suppose your family went to a dinner buffet and all of you had stomach problems afterward. Different people might have eaten different things, but suppose the only thing that everybody has eaten was raw oysters. It would be reasonable to infer that the oysters caused the stomach problems. For another example, consider patients who suffer from AIDS, which weakens the immune system and makes deadly infections more likely. Despite their different backgrounds, it was discovered that all AIDS patients have been infected by HIV. So the conclusion was that HIV causes AIDS. The method of agreement is commonly used in causal reasoning, but note that if we discover a cause using this method, it does not tell us whether the cause is causally sufficient for the effect. In other words, the identified cause on its own might not be enough to bring about the effect. Even though we now know that HIV causes AIDS, this does not mean that everyone with HIV must get AIDS. In fact many people with the virus have not developed AIDS. Understanding why this is the case will help us find a cure for AIDS. 14.2 THE METHOD OF DIFFERENCE If one group of situations leads to an effect E, but another group does not, and the only difference between the two groups is that C is present in the former but not the latter, then C is the cause of E. Suppose a mobile phone is not working, but it works fine when the battery is replaced. Since the only thing that is different is the battery, it was probably the

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cause of the problem. Consider also the table above. We cannot apply the method of agreement because A and C are both present when E occurred, so the rule does not tell us which is the cause. But applying the method of difference, E did not occur in situation 3, and the only difference with #1 and #2 was the absence of C. So we can infer that C is the cause of E. The method of difference appears to be rather simple, but it plays a very important role in science, often under the guise of control experiments. In a control experiment in which you want to investigate if C is the cause of some effect, you set up two experimental situations that are exactly the same, except that C is present in one but not the other. Suppose you add some fertilizer to a plant and you notice that it grows extremely tall. How can you be sure that it is the fertilizer that caused it to grow quickly and not the water or the soil in which the plant is grown? A good control experiment is to place an identical plant (the so-called control group) next to it and give it the same water and soil, keeping everything the same except that it does not get any of the fertilizer. If it does not grow as quickly, then we can conclude that the fertilizer was indeed the cause. In conducting a control experiment, it is important to make sure that you keep every variable the same other than the condition that is suspected to be the cause. If for example you use a different type of plant as your control group, and put it in a different room, then if it does not grow as tall it might simply be due to the nature of the plant or the different environment (for example, less sunshine), and not the lack of the fertilizer. Of course, it might be difficult and expensive to ensure that all relevant conditions are the same in a control experiment. To show that playing the piano improves a child's IQ, you need to find two groups of children who are exactly the same except that one group learns the piano and the other group does not, and check whether there is a bigger increase in IQ in the first group. But children have different family backgrounds, personalities, and innate intelligence, so it is of course impossible to ensure that the two groups are exactlythe same. What psychologists can do is to control for the differences by ensuring that the two groups are as similar as possible, or use special statistical techniques to analyze the results. But even though good control experiments are hard to come by, they are crucial for obtaining trustworthy results. (See also the discussion of control experiments in medicine on page 136.)

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14.3 THE JOINT METHOD Suppose one group of situations leads to an effect E, but another group does not. If C is the only factor common to situations in the first group, and it is also the only factor that is absent from all the situations in the second group, then C is the cause of E.

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In a way, the joint method is a combination of both the method of agreement and the method of difference. If you look at the table above carefully, you will see that neither the method of agreement nor the method of difference can be applied directly. Situations 1 and 2 have more than one candidate cause in common, so no conclusion can be drawn about the cause. The method of difference cannot be applied because the three situations differ in more than one candidate causes. But combining both methods, we end up with a more powerful rule, which can be applied to this example. This joint method can be formulated more simply as follows: If C is the only candidate cause that is present when and only when E occurs, then C causes E.

14.4 THE METHOD OF CONCOMITANT VARIATIONS If variation in some factor C is followed by variation in an effect E, then C is the cause of E. Situation

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The general idea behind this principle is that an effect can change by changing its cause. Suppose the number of people suffering from asthma attacks goes up when air pollution becomes very bad. When air quality improves, the number of

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such attacks drops. Because there is this correlation in variation, we conclude that air pollution causes asthma attacks. A version of the method of concomitant variations is employed in medicine to investigate whether certain substances have a beneficial or harmful effect. To show that an effect exists, we look for a dose-response relationship, showing that the size of the effect is affected by the amount of the substance. For example, to show that mercury is toxic, we provide evidence that a larger amount of exposure to mercury (dose) is followed by more severe allergic reactions or nerve damage (response). Note that the application of the method does not require that an increase in C must always correspond to an increase of E. The relationship can also be an inverse one, such as increasing the dosage of a painkiller decreases the number of headaches. What is important is that variation in the cause has some predictable linkage to variation in the effect.

14.5 THE METHOD OF RESIDUES If a set of conditions causes a range of effects, and some of the effects can be explained by some of the earlier conditions, then the remaining effects are caused by the other remaining conditions. The idea behind the method of residues is to identify causes by elimination. Suppose you discover that two books are missing from your room, and only two people have been there recently. You ask one of them and he confesses that he "borrowed" just one book without asking. If you trust his answer it would then be reasonable to conclude that the other visitor had taken the second book. As Sherlock Holmes said in one of the detective novels, "When you have eliminated the impossible, whatever remains, however improbable, must be the truth." The method of residues is often used to discover new causes. If we can explain only part of an effect, it might be because there is some unknown cause that plays a role. This was actually how the planet Neptune was discovered. In the 19th century, astronomers could account for the orbits of all the planets known at that time except for Uranus. Leverrier, a French mathematician, concluded that there must be some other cause that explain Uranus's special situation. He thought this could only be explained if there was an unknown planet that affected Uranus, and it eventually led to the discovery of Neptune. 14.6

LIMITATIONS OF MILL'S METHODS

Mill's methods should come as no surprise, as these rules articulate some of the principles we use implicitly in causal reasoning in everyday life. But it is important to note their limitations: • The true cause might not be any of the candidate causes. Mill's methods start with a preselected set of candidate causes. If the true cause of the ef-

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feet is not among them, obviously the five rules will not yield the correct result. Of course, we can always expand or change the list of candidate causes. But Mill's methods will be more effective when we already have a good idea about what the possible causes of the effect might be. • The effect might have more than one cause. Mill's methods can fail spectacularly when more than one candidate cause can bring about the same effect. It might be true that everybody who ate oysters got sick. But perhaps the oysters were fine, and it was the salad and the noodles that had gone bad. It just so happened that everyone ate either salad or noodles. But the method of agreement will give us the wrong result.1 • Causation can be indeterministic. Throwing a rock at a window might cause it to break, but not always. A heart attack can result in death, but again not every time. Mill's methods can give the wrong results when dealing with probabilistic causes. Take the joint method for example, where the cause is supposed to be the condition that occurs when and only when the effect is present. This rules out causes that do not determine their effects but that make them highly probable. Having noted some of the limitations of Mill's methods, it should be said that they remain important tools of scientific reasoning. They do not guarantee that you will find the real cause of an effect, but they are good heuristics to try out in causal investigations. EXERCISES 14.1

Which of Mill's method is used in the following pieces of reasoning? a) Pressure decreases productivity, because the more pressure I suffer from, the less work I am able to do. b) You were fine when you ate the pudding last week. The pudding this week was no different, except that I put in alcohol. So if you had an allergic reaction this time it must have been the alcohol. c) Amie thinks that drinking warm milk before bed makes her sleep better. She tried lots of things like listening to relaxing music, meditation, reading a book, and even combinations of these methods. But every time after drinking warm milk she slept soundly, and nothing else worked. d) Two identical cars were being driven in the same way along the same route, except that one of them has less pressure in the tires. It turns out that this car ends up using more fuel to travel the same distance. So inadequate tyre pressure causes a higher fuel consumption.

1 Mill's methods can actually be used to identify causes that are combinations of events. What we need to do is to expand the list of candidate causes so that it includes combination of events, such as "salad or noodles" being one single candidate cause. But we might need to consider more situations before we can conclude which event or combination of events is the cause.

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14.2 Consider the table in Section 14.3 used to illustrate the joint method. Was any situation redundant? In other words, was there any situation in the table that could have been removed, but the same conclusion could still be derived using the resulting information? 14.3 In each table below, find the cause of E and explain which of Mill's methods is being used. If none of them can be applied, explain why. a) Situation

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Are these statements true or false? a) In every situation in which the method of difference gives the correct answer, the joint method will also give the correct answer. b) To apply the method of difference, we need information about at least two different situations, one in which the effect occurred, and the other in which it did not.

CHAPTER 15

REASONING ABOUT CAUSATION

In the last chapter we discussed Mill's methods and their limitations. Here are some further issues to consider about causation. In many situations, causes are correlated with their effects. An event C is said to be positively correlated with E when the presence of C increases the probability that E will also occur. C is said to be negatively correlated with E when C decreases the probability of E. If C has no effect on the probability of E, then C is not correlated with E, or C is independent of E. So for example, the appearance of lightning is positively correlated with thunder, negatively correlated with a clear sky, and presumably not at all correlated with the day of the week. Correlation is about how often two things are associated with each other, so it is a matter of degree. Lightning is inevitably followed by thunder,1 and there is no thunder without lightning. This is 100% or a perfect correlation. Smoking is positively correlated with lung cancer, but obviously not all smokers will get cancer. Indeed, a low correlation between two types of events does not rule out causation in particular instances. A hunter might fail to shoot his prey most of the time, but when he succeeds his shot will be the cause of the animal's death. 'Although you might be too far away to hear it. An Introduction to Critical Thinking and Creativity: Think More, Think Better. By Joe Y.F. Lau Copyright © 2011 John Wiley & Sons, Inc.

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Similarly, most people are fine after taking aspirin, and there is only a low positive correlation between aspirin and allergic reactions. But aspirin does cause allergic reactions in about 1% of the population. If a low correlation does not preclude causation, then is a high correlation sufficient for causation? Not at all! Confusing positive correlation with causation is a common mistake in causal reasoning. Even if C does not cause E, there can be many reasons why C is positive correlated with E. Here are the main possibilities: • The correlation between C and E is purely an accident. • E causes C and not the other way round. • C does not cause E but they are the effects of a common cause. • The main cause of E is some side effect of C rather than C itself directly. This is not to say that data about correlation are irrelevant to causation. As a matter of fact correlation is often a guide to causation. But we need to rule out the alternative possibilities listed above if we want to infer causation on the basis of positive correlation. Let us discuss these cases further. 15.1 15.1.1

WHY CORRELATION IS NOT CAUSATION Accidental correlation

Sometimes high correlation is the result of not having enough data. Suppose I have been in only one car accident my whole life, and that was the only time I ever wore red trousers. There is a perfect correlation between the color of my trousers and my being involved in a car accident, but this is just a coincidence. Correlation data are more useful when they involve a large range of cases. But still we need to be careful. It has been suggested that the sea level in Venice and the cost of bread in Britain have both been generally on the rise in the past two centuries (Sober, 1988). But it is rather implausible to think that the correlation is due to some underlying causal connection between the two cases. The correlation is presumably an accident due to the fact that both have been steadily increasing for a long time for very different reasons. There is also a kind of accidental correlation known as spurious correlation (or Simpson's paradox) that has to do with the aggregation of statistical data. It is a rather interesting but somewhat technical topic. If you are interested you can read more about it on our companion website. 15.1.2 The causal direction is reversed Sometimes C is correlated with E not because C causes E, but because E causes C. Drug users are more likely to suffer from psychiatric problems. This might be because drug use is the cause, but perhaps preexisting psychiatric problems cause people to turn to drugs. Correlation by itself does not tell us which of these

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two stories (if any) is correct.2 It is important to bear this in mind when reading newspaper accounts of scientific research. Scientific research might tell us only that drug use is positively correlated with psychiatric problems, but reporters who should know better might instead write, "drugs make you depressed and crazy." The word make suggests causation but this might not actually be supported by the data. When two causal factors or variables reinforce each other, we have a causal loop. For example, there is a correlation between health and GDP growth in many countries. This is because on one hand, healthy citizens work longer and better, contributing to economic growth. On the other hand, higher GDP brings about better living conditions and medical care, improving health as a result. So health and GDP growth are mutually reinforcing. It is possible that one variable has a more significant effect on the other. However, it would require sophisticated statistical techniques to determine which is which. A vicious circle happens when a causal loop makes a bad situation even worse. Take stage fright for example. Becoming nervous and stressful when you are performing can make you perform less well, and this might in turn make you even more nervous, affecting your performance further. Catastrophe ensures if the vicious circle is not broken.

15.1.3 Hidden common causes Sometimes C and E are correlated not because one causes the other but because there is a hidden condition X that causes both C and E. For example, children who wear bigger shoes tend to have better reading skills. Do shoes somehow promote brain growth? Presumably not. The more mundane explanation is that older children read better, and they have bigger feet. So growth is the hidden common cause that leads to both bigger shoes and better reading skills. Or suppose the drinking of botded water instead of tap water is correlated with healthier children. Is this because bottied water is cleaner, and ordinary tap water contains harmful impurities? Not necessarily. Perhaps this is just because wealthier parents can afford higher-quality care and food for their children, and being more cautious, they choose to buy bottled water even if tap water is just as good.

15.1.4 Causation due to side effect In some cases where C correlates with E because C occurs together with some other condition or side effect that actually causes E. The causal contribution from C to E might be nonexistent or of lesser importance. The placebo effect is a good example of causation due to side effect. It refers to the real or felt improvement in a patient's condition that is due to beliefs about the treatment rather than the medical efficacy of the treatment itself. It is suggested that when patients believe that they have taken medicine, this is enough to make many of them feel better or Most likely there is causation in both directions.

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suffer from less pain, even when the treatment being given (such as a cornstarch pill) has no medical benefit. In fact, it has been reported that a larger pill has a more pronounced placebo effect, and colored pills are better than white ones, and that injections are even better! The extent and mechanism of the placebo effect is still under study, but this is one reason why it is necessary to include a control group in testing a drug. Subjects in the control group would be given an inert pill without being told that this is the case, and the difference in response in the normal and control groups can then provide a more reliable estimate as to the effectiveness of the drug.3

Placebo Surgery It is surprising that the placebo effect applies not just to drugs but to surgery as well. In Moseley et al. (2002), over 100 patients suffering from a knee problem (osteoarthritis) were given either real surgery or fake surgery (in which the knee received only a superficial cut). The patients were not told whether they were given a real surgery or not. But in the following two-year period, both groups reported the same amount of pain and improvement in function. In another study, researchers studied whether transplanting human embryonic cells into the brain would improve Parkinson's disease (McRae et al., 2004). All the patients had small holes drilled into their skulls. Half of them were given the transplant, but the patients did not know whether they had it or not. Yet a year later, those who believed that they had the real transplant reported a better quality of life, whether or not they actually had the surgeryl This is a powerful demonstration of the placebo effect, and a good reminder of the importance of double-blind studies. It also raises a difficult ethical question: Should doctors exploit placebo effects more often in medical treatments? But is it ethical to lie to patients about the nature of their treatment?

In scientific research, it is important to investigate side effects to ensure that experimental results are reliable. For example, studying captive animals might not give a true picture of the behavior of wild animals because putting animals in a confined environment might change their habits, which is a form of side effect. In other situations, experimental procedures can introduce contamination or artifacts that affect the results. The following are other cases of side effect causation relating to human beings: An even better version of this approach is to adopt a double-blind study in which neither the patient nor the doctor know whether the real pill or the fake one has being given. This is to avoid the doctor leaking relevant information to bias the expectation of the patient.

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GOOD EVIDENCE FOR CAUSATION

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• An example in social science and industrial psychology is the Hawthorne effect. This refers to the fact that people tend to change their behavior when they know they are being studied. In particular, they might work harder or perform better in an experimental setting. • People react to new things differentiy, and this produces a novelty effect. Once the novelty wears off, their behavior might return to normal. For example, some schools claim that students behave better and learn better when they switch their drab school uniforms to colorful Hawaiian shirts. Although there might have been a real correlation between the colorful shirts and the better performance, this might just be due to the novelty of the new arrangement. To show that wearing Hawaiian shirts can somehow really improve learning and behavior, we would check whether the improvement still remains after the novelty is gone. • The pygmalion effect originated from a study where teachers were told that some of their students were above average even though they were randomly selected with the same average abilities. But the subjective expectation of the teachers somehow led to better performance by these students later on. The result has been replicated in other contexts, and this has important implications for education and management. 15.2

GOOD EVIDENCE FOR CAUSATION

We have looked at many reasons why correlation might not amount to causation. To establish causation then, it is important to eliminate these alternative hypotheses. But what kind of positive evidence can we obtain to support causation? 15.2.1

Look for covariation and manipulability

First of all, data about covariation are particularly useful. Recall Mill's method of concomitant variations. If changes in one event correspond to changes in another event, then this makes it more probable (though not conclusive) that one causes the other. When we suspect smoking causes lung cancer, the fact that cigarette smokers have a higher cancer rate than nonsmokers is only one piece of evidence. It becomes even more convincing when it is discovered that the death rate from lung cancer increases linearly with the number of cigarettes smoked per day. Covariation is even stronger evidence when it can be directly manipulated and not just being passively observed—we vary some aspects of the cause and see how it affects the effect. For example, hitting the key of a piano causes a sound to be made. We can be sure of the causal connection because we can change the timing and the loudness of the sound by controlling when and how we hit the piano key. This makes it extremely unlikely that the correlation is accidental or due to some other explanation. In reality, manipulating correlation can sometimes be difficult or even unethical to do. To study how smoking leads to lung cancer, it would be

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immoral to request some subjects to smoke more cigarettes and see if they are more likely to get cancer!

15.2.2

Look for a reliable model of causal mechanism

A causal mechanism is a series of objects, processes, or events that explain how a cause leads to its effects. Using the piano as an example again, hitting the key causes a felt-covered hammer to strike a steel string. This causes the string to vibrate, and the vibration in turn causes air molecules to move, which is the sound we hear. This causal process explains how the keys can create music, and a breakdown in any step of the causal process might result in no sound being produced. Nearly all instances of causation involve underlying causal mechanisms.4 A causal mechanism explains why there is causation and helps us make predictions about what would happen when the system changes. For example, the story about the causal mechanism in a piano explains why a louder sound is heard when we hit the key harder, because this means the string would vibrate with a larger amplitude, making a louder sound. This is why the search for causation is often tied to the search for causal mechanisms. One way to show that C causes E is to offer a theory of causal mechanism that leads from C to E, and try to provide evidence to support this theory. This way of establishing causation is particularly important when we are dealing with events that are difficult or impossible to repeat. Of course, it is possible to obtain strong evidence for causation even when we lack detailed knowledge of the underlying mechanism. For example, we now know that infection by HIV is the cause of AIDS, but this discovery took place before detailed knowledge of how it is that the virus causes AIDS through interfering with the immune system, and even up till now there are still gaps in our understanding of the exact causal mechanism. Similarly, it has long been known that there is a correlation between smoking and lung cancer, but it took nearly 50 years to identify the causal mechanisms whereby the chemical compounds in cigarette smoke trigger the cellular changes that result in lung cancer.

15.3

CAUSATION IS COMPLICATED

We have discussed a lot about searching for the cause of an effect. However, the world is a complicated place and events can interact with each other, often making it difficult if not impossible to find the one true cause. Here are some useful terms for making more fine-grained distinctions between causes: 4

Nearly all, because there might be exceptions when it comes to causation in quantum mechanics involving action-at-a-distance, where remote particles seem to be able to affect each other without any apparent causal mechanism. There is also the philosophical question of whether there is a most basic level of causal mechanism.

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• Causal relevance: Suppose a student failed a course. She might have been lazy or having personal problems. Or perhaps she was ill on the day of the exam. All these factors could have contributed to her failure. They were all causally relevant, each being a cause of her failure but none being the cause. The most important one is the primary or central cause. • Causally necessary and sufficient conditions: X is causally necessary for Y when Y would not happen without X, and X is causally sufficient for Y when X by itself is enough for Y. Water is causally necessary but not sufficient for our survival, and moving electric charges are sufficient but not necessary for the presence of a magnetic field.5 But X can be causally relevant to Y even if X is neither causally necessary nor sufficient for Y. • Triggers: A triggering cause (or trigger) is a cause that starts off a chain of events leading to an effect. Whereas a structural cause (or standing condition) is a background condition that is causally relevant to the effect but which on its own is not sufficient for it. For example, an electric spark in a kitchen with a gas leak can result in an explosion. Here, the spark is the trigger, and the flammable gas is the standing condition. • Proximity: A proximate cause happened at a time near the occurrence of the effect, whereas a distal cause happened much earlier. • Randomness and causal determination: A random event is one that is not causally determined by what happened earlier. To say that an event is determined is to say that it must occur given what has happened earlier and the physical laws of our universe. EXERCISES 15.1 For each of these correlations, think of at least two alternative causal explanations. a) Children who eat breakfast perform better at school. b) A six-year study of more than a million adults ages 30 to 102 showed that people who get only 6 to 7 hours of sleep a night have a lower death rate than those who get 8 hours of sleep. c) There is a moderate correlation between milk drinking and cancer rate across societies. d) Smokers are 1.6 times more likely to think of killing themselves than non-smokers. e) Students who smoke are more likely to have lower grades at school. f ) Students who use Facebook more often have lower grades. g) People who smile sincerely more often tend to live longer. h) People who go jogging regularly are less likely to suffer from depression. 5

A simple magnet can produce a magnetic field without electricity.

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i) Teenagers who use alcohol, marijuana, or other illegal drugs are much more likely to experience psychiatric disorders, especially depression, in later years. 15.2 Which of these conditions are mutually reinforcing? Can you give some more examples? a) stock prices going down, panic selling b) heating a piece of metal, the piece of metal expanding c) anxiety, not being able to sleep 15.3 According to Reichenbach, a famous philosopher, if two events X and Y are correlated, then either X caused Y, or Y caused X, or they are the joint effects of a common cause. What is wrong with this claim according to the principles discussed in this chapter? 15.4 The philosopher John Mackie proposed this theory of causation: X causes Y = X is an insufficient but necessary part of a condition that is itself unnecessary but sufficient for Y. a) Suppose Akiko stepped on Bella's toe and this caused Bella's toe to bleed. Explain how this example of causation satisfies Mackie's definition. b) Can you think of any counterexample or objection to the proposal? This is a difficult question, but do give it a try! 15.5 Can you give an example where an event X is causally relevant to Y even though X is neither causally necessary nor sufficient for F? 15.6 Ê3 See if you can come up with examples of causal mechanisms from the subjects that you have studied or are familiar with.

CHAPTER 16

DIAGRAMS OF CAUSAL PROCESSES

Causal processes are often complicated. Here are some diagrams that can make them easier to understand. They are also useful in giving presentations.

16.1

CAUSAL NETWORKS (^~~ climate change industrialization Cü^extreme weather deforestation C^soilf more floods C|__less farmland

In a causal network diagram, nodes represent events and arrows link causes to effects. The diagram above shows the process of soil erosion. We can also use An Introduction to Critical Thinking and Creativity: Think More, Think Better. By Joe Y.F. Lau Copyright © 2011 John Wiley & Sons, Inc.

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annotated arrows to provide more information about the causal links. For example, a positive sign [+] next to an arrow linking A to B indicates that A increases the probability of B. A negative sign [-] indicates that A decreases the probability of B. One might even assign numerical probabilities. With enough information, we can calculate the probabilities relating other events, and predict how the system respond to changes. This is known as a Bayesian network or Bayes net. But causal diagrams are not just for scientists. They are useful for showing causal interactions in many other areas. For example, a diagram might use arrows to link together different art movements to show how they have influenced each other. 16.2

FISHBONE DIAGRAMS

The diagram below shows the general structure of a fishbone diagram, so-called because of its shape: causal factor #1

causal factor #3

causal factor #2

causal factor #4

These diagrams are also called cause and effect diagrams, and they were made popular by Kaoru Ishikawa, a Japanese professor who used them in quality management. Such diagrams help us visualize and classify the causal factors that contribute to an effect. We start with a diagram that resembles a fish skeleton and place the problem or issue to be investigated at the fish head. We then add branches corresponding to different categories of causal factors. Specific factors under a category are then listed along the branches. The following example shows some of the main reasons why a user ends u p taking a blurry photo with a camera: HARDWARE

ENVIRONMENT subject moving too fast

dirty lens too dark

wrong lens

blurry photo wrong exposure

shaky hands

out of focus 'wrong mode METHOD

not following instruction USER

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A fishbone diagram is useful when it is possible to provide a simple classification of the different types of causes that lead to an effect. The choice of categories is crucial if the diagram is to provide an informative analysis of the overall situation. For example, if you want to improve your performance in a certain area, the relevant categories might include skill, training, environment, and personality. Here are some standard ones in business and management: Acronym

Field

Categories

6Ms

manufacturing

machines, methods, material, measurements, manpower (people), mother nature (environment)

4Ps

service industries

policies, procedures, people, plant (technology)

4Ps

marketing

product, pricing, promotion, place

16.3

FLOWCHARTS

A flowchart is a diagram using connected shapes to represent the steps of a complex process, some of which might involve actions and decisions. The example below describes how a busy person ruthlessly deals with the flood of emails in his inbox:

reply immediately

The chart says that unimportant emails are deleted. Important but nonurgent ones are set aside to be replied later. Otherwise a reply is sent right away. Originally, flowcharts were used in computer science to describe the different steps of a computer program. But because flowcharts are useful for describing

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complex procedures, they are now routinely used in many other areas as well, from customer service to medical diagnosis. Writing down a flowchart forces us to be clear about the different steps of a procedure. It can then be used as the basis of discussion, to see how a process can be improved. It can be also used as a recipe for different people to follow to ensure uniformity in how a task is to be completed. Furthermore, if more than one person is involved in completing a task, we can use a flowchart to assign people different parts of the task, so that each person knows exactly what his or her responsibilities are. EXERCISES 16.1 Suppose someone thinks that playing violent video games does not cause violent behavior. Rather, having a violent personality causes people to play lots of these games and engage in violence. Draw a causal network diagram showing the causal processes involved. 16.2 Consider these five steps for a pedestrian to cross the road safely, in random order: "look left and right," "stop at the curb," "walk across quickly," "wait a few seconds," "check if the road is clear" Draw a flowchart for the whole process using only these steps. 16.3 E3 Go online and search for "getting things done flowchart." Getting Things Done is a system created by David Allen that helps people become more systematic and productive at managing tasks. If you do not know what it is, look at the flowchart and read a bit more to see what the different steps are. See if this system is useful for you. 16.4 Kl To find out more about the meanings of the different flowchart symbols, do an Internet search on "standard flowchart symbols." 16.5 IEI Draw a causal network diagram and a fishbone diagram for a topic that you are interested in.

CHAPTER 17

STATISTICS AND PROBABILITY

Many people think of statistics as a scary subject involving lots of numbers and equations. While it is true that statistics can be quite technical, the subject remains highly relevant to modern life. For example, before booking a hotel, we might check the number of good and bad online reviews. When we make investment decisions, we might also review the relevant financial and statistical data first. In this chapter we shall discuss some general principles for interpreting statistical studies, without going too much into the mathematical details. Many statistical studies investigate samples. We study a sample to infer general conclusions about a population, the set of things we are interested in. Suppose we want to find out whether heavy metal contamination in vegetables is a serious problem in China. The population is then all the vegetables in the whole of China. But it is obviously impossible to test all of them. So instead we collect a variety of vegetables from different places in China. This is our sample and we shall measure the amount of heavy metal contaminants in this batch. If the study is done well, it will give us a good picture of the overall situation in China. However, if the study is not done correctly, it might not just be a waste of time and money. Policy decisions based on a bad study can have harmful consequences.

An Introduction to Critical Thinking and Creativity: Think More, Think Better. By Joe Y.F. Lau Copyright © 2011 John Wiley & Sons, Inc.

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17.1 EVALUATING SURVEYS AND SAMPLING STUDIES Here are some questions we should ask if we want to evaluate a statistical study.

17.1.1 What exactly is the finding? What do the keywords mean? First of all, focus on the main conclusion. What is the significance? What is the most important finding? How is it formulated? How are the keywords defined? • Distinguish between the actual results and their interpretation. For example, many reports confuse correlation with causation. A blog article might say that sleeping more makes your life shorter, which is a claim about causation. But the actual statistics might tell us only that adults who sleep 8 or more hours a day have a higher death rate than those who sleep 6 to 7 hours. These correlational data are not about causation at all. (Perhaps less healthy people sleep more, so sleeping more does not directly cause death.) • Check the definitions of key concepts. A survey might say that 27% of university students are Christians. But what does being a Christian mean? Is it just a matter of saying that you are? Or does it involve regular church attendance? Is a Mormon a Christian? Statistics are more informative when it is clear how the main variables are actually measured and defined.

17.1.2 How large is the sample? When we extrapolate from a sample to the population, a larger sample is likely to give a more accurate conclusion. If a restaurant wants to find out whether its customers enjoy the food and service, it would not be enough to solicit the view of just one customer. On the other hand, spending extra money and time on a larger sample size might not be worth it if a smaller one would do just as well. It is not easy to determine the optimum sample size. Partly it depends on the size of the population and the level of precision required of the results. (See Section 17.1.5 below.) Other relevant factors include the variability of the population.

17.1.3 How is the sample chosen? How the sample is selected affects greatly the reliability of the conclusions. A sample should be representative of the population, in the sense that the features being studied are distributed in the same way in both the sample and the population. If you want to find out how often people exercise, it would be wrong to interview only people at the local gym, since they probably exercise a lot more. This constitutes what we call a biased sample. We should check carefully how a sample is chosen to see if there are hidden biases. For example, some online surveys allow people to submit their opinions more than once. They might also attract people who are more computer savvy, have more free time, and are more willing to give their opinion.

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A good way to minimize biased sampling is through random sampling, by which each sample is selected randomly from the population. Given an adequate sample size, this method is highly likely to result in a representative sample. But even with random sampling, we should be careful of potential biases in the results due to the fact that some selected individuals might not be reachable (for example, in a telephone survey) or are not willing to participate.

Statistics and advertisements Many advertisements cite statistical surveys. But we should be cautious because we usually do not know how these surveys are conducted. For example, toothpaste manufacturer Colgate once had a poster that said "More than 80% of dentists recommend Colgate." This seems to say that most dentists prefer Colgate to other brands. But it turns out that the survey questions allowed the dentists to recommend more than one brand, and in fact another competitor's brand was recommended just as often as Colgate! No wonder the UK Advertising Standards Authority ruled in 2007 that the poster was misleading and it had to be withdrawn. A similar case concerns a well-known cosmetics firm marketing a cream that is supposed to rapidly reduce wrinkles. But the only evidence provided is that "76% of 50 women agreed." But what this means is that the evidence is based on just the personal opinion from a small sample with no objective measurement of their skin condition. Furthermore we are not told how these women were selected and whether there was any double-blind study conducted. Without such information, the "evidence" provided is pretty much useless. Unfortunately such advertisements are quite typical, and as consumers we just have to use our own judgment and avoid taking advertising claims too seriously.

17.1.4

What method is used to investigate the sample?

If a sample is investigated using a biased method, the statistical results can be unreliable even if the sample is representative. There are various ways this might come about: • Social desirability: Suppose a teacher selects some students randomly and asks whether they have cheated in exams. This survey will underestimate the extent of cheating since students are unlikely to admit to cheating to their teacher. We generally want to portray ourselves positively and are reluctant to confess to undesirable attitudes or activities. This is especially true when we are questioned directly or when we have doubts about the confidentiality of the results.

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• Leading questions: These are questions that are formulated in such a way that answers are likely to be skewed in a certain direction. For example, "Do you want to give vitamin pills to your children to improve their health?" is likely to solicit more positive answers than the more neutral "Do you intend to give vitamin pills to your children?" (See also the discussion about anchoring in Section 20.2.1.) • Observer effect: It is often difficult to conduct a statistical study without affecting the results in some way. People might change their answers depending on who is asking them. Animals change their behavior when they realize they are being observed. Even measuring instruments can introduce errors. We just have to be careful when we interpret statistical results.

17.1.5 What about the margin of error? Many statistical surveys include a number known as the margin of error. This number is very important for interpreting the results. The concept is a bit difficult to grasp, but it is worth the effort, especially if you are a journalist or someone who has to report statistics or make decisions based upon them. The margin of error arises in any sampling study because the sample is smaller than the whole population, and so the results might not reflect the reality. Suppose you want to find the average weight of a Korean by weighing a random sample of Koreans. The average weight of your sample would be the statistical result, which might or might not be the true result—the average that is calculated from the whole Korean population. If you do manage to weigh the whole population, then your statistical result will be the same as the true result, and your margin or error will be zero indeed (assuming there are no other sources of error like faulty weighing machines.) When the sample is smaller than the population, the margin of error will be larger than zero. The number reflects the extent to which the true result might deviate from the estimate. The margin of error is defined with respect to a confidence interval. In statistics, we usually speak of either the 99% confidence interval, the 95% confidence interval, or the 90% confidence interval. If the confidence interval is not specified, it is usually (but not always!) 95%. Suppose an opinion poll about an upcoming election says that 64% of the people support Anson, with a margin of error of 3%. Since the confidence interval is not mentioned, we can assume that the margin of error is associated with the 95% confidence interval. In that case, what the poll tells us is that the 95% confidence interval is 64 + 3%. What this means is that if you repeat the poll 100 times, you can expect that in 95 times the true result will be within the range specified. In other words, in 95% of the polls that are done in exactly the same way, the true level of support for Anson should be between 61% and 67%. There are at least two reasons why it is important to consider the margin of error. First, if the margin of error is unknown, we do not know how much trust we should place in the result. With a small sample size and a large margin of error, the

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true result might be very different from the number given. The other reason for considering the margin of error is especially important when interpreting changes in repeated statistical studies over a period of time, especially opinion polls. Suppose 64% of the people support Anson this month, but the number drops to 60% the next month. How seriously should we take this to indicate that support for Anson is slipping away? If the margin of error is say 5%, then the new finding is within the 95% confidence interval of the earlier result (64 ± 5%). It is therefore quite possible that there is actually no change in the opinion of the general public, and that the decrease is due only to limited sampling. Finally, it should be emphasized that the margin of error does not take into account biases or methodological errors in the design and execution of the study. So these problems can still be present in a result with a low margin of error!

17.2

ABSOLUTE VS. RELATIVE QUANTITY

When we interpret statistics, it is important to distinguish between absolute and relative quantity. Absolute quantity refers to the actual number of items of a certain kind. Here are some examples: • The number of female professors at Beijing University. • The number of computer programmers in India. On the other hand, a relative quantity is a number that represents a comparison between two quantities, usually a ratio or a fraction, or a number that measures a rate comparing different variables: • The ratio between female and male professors at Beijing University. • The percentage of computer programmers among workers in India. This distinction is important because meaningful comparisons often require information about the right kind of quantity. Suppose the number of violent crimes this year is a lot higher than that of 10 years ago. Does it mean our city has become more dangerous? Not necessarily because the higher number could be due to the increase in the population. We need to look at the relative quantity, such as the number of violent crimes per 1,000 people. If this number has actually dropped over the same period, the city has probably become safer despite the higher number of crimes! Similarly, drivers between the age of 20 and 30 are involved in more car accidents than drivers who are between 60 and 70. Is this because older people drive more safely? Again not necessarily. There might be more younger drivers, and they might also drive a lot more. We should compare the number of car accidents per distance traveled rather than the absolute number of accidents.

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A misleading use of relative quantity In April 2010, an oil rig in the Gulf of Mexico owned by British Petroleum (BP) exploded and a huge amount of oil started leaking from the deep sea and BP was unable to stop the spill. In a newspaper interview, Tony Hayward, who was the chief executive of BP, tried to downplay the consequences of the leak. He said that the amount of leaked oil and dispersant used to tackle the oil slick is small compared with the very big ocean (Martel, 2010): The Gulf of Mexico is a very big ocean. The amount of volume of oil and dispersant we are putting into it is tiny in relation to the total water volume. This is a rather disingenuous use of relative quantity. The amount of spill might be rather small compared with the total volume of the ocean in the Gulf of Mexico, and even smaller when compared with all the water in the world, but it is still a huge amount of pollution that can affect a lot of people and animals and bring about terrible environmental destruction.

The absolute vs. relative distinction is particularly important in healthcare. The risks associated with illnesses, drugs and medical treatments can often be specified in absolute or relative terms. Take these two headlines: • New miracle drug lowers liver cancer risk by 50%! • New drug results in 1% drop in liver cancer risk! The first headline is presumably a lot more impressive, but both can be correct in describing the result of a clinical trial. Imagine two groups of normal people, 100 in each group. The first group took the drug to see if it reduced the number of liver cancer. After 10 years, 1 out of 100 developed liver cancer. The other control group took a placebo pill and 2 out of 100 had liver cancer after 10 years. The absolute risk of getting liver cancer is 2% for those without the drug, and 1% for those taking the drug. So the second headline correcüy describes the reduction in absolute risk. But reducing 2% to 1% amounts to a relative risk reduction of 50%. So the first headline is correct as well. Why should we care about whether risk information is presented in absolute or relative terms? First of all, note that information about relative risk tells you nothing about absolute risk. If eating farmed salmon increases your chance of getting a certain disease by 100%, this sounds very scary. But this relative increase tells you nothing about the absolute likelihood of getting the disease. If the disease is extremely rare, the chance of getting it can remain negligible even after it has been doubled.

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So be careful of advertisements for drugs and medical treatments. The two headlines above give very different impressions. Hasty decisions based on incomplete data can be dangerous, especially because drugs and treatments can have undesirable side effects. If taking the new liver cancer drug causes more headaches and other health problems, the 1% reduction in absolute risk might not be worth it. 17.3

MISLEADING STATISTICAL DIAGRAMS

Diagrams can often make it easier to understand and summarize statistical data. Trends and patterns can become more prominent. But the suggestive power of diagrams can also be abused when data are presented in a misleading way. Here are some common tricks that we should be aware of. First, when a chart has horizontal and vertical axes, check the origin of the axes carefully to see whether they start from zero. Take these two diagrams below: profit (million $) 12.0

profit (million $) 20

2006 2007 2008 2009 year

2006 2007 2008 2009 year

The two diagrams present the same data regarding the profit earned by a certain company from 2006 to 2009, the only difference being that the vertical axis of the diagram on the left does not return to zero. A careless person taking a quick glance at this diagram might get the impression that profit has dramatically increased a few times over a few years, when in fact it has only increased slightly. Obviously, if a chart fails to label the axis, then it is even worse! Apart from the origin of an axis, we should also check its scale. Consider this diagram showing the number of cakes sold by a shop from 2000 to 2008:

cakes sold 4000 3000 2000 1000 ■+-

4-

4-

-4-

-+- 01 02 07 08 year 2000

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On the face of it, the picture seems to indicate that there was a sudden surge in cake sales. But this is actually an illusion because the horizontal time axis is not evenly scaled. The period 2002 to 2007 is compressed compared to the other periods, giving the erroneous impression that the rate of growth has abruptly increased when in fact the growth in sales might have been rather steady.

» (D

1980: 9,947 calls 2000: 50,105 calls The diagram above shows that the number of emergency calls received by a hospital has increased about fivefold between 1980 and 2000. This is represented pictorially by the fact that the diagram on the right is five times taller than the left one. But the problem is that subjectively, our perception of the relative difference depends on the area instead of just the height. Since the diagram on the right is also five times wider, its area is actually 5 x 5 = 25 times larger than the diagram on the left. The result is that looking at such the diagram, the readers have the impression that the increase is a lot more than just five times. 17.4

PROBABILITY

It is no exaggeration to say that probability is the very guide to life. Life is full of uncertainty, but we have to plan ahead based on assumptions about what is likely or unlikely to happen. In all kinds of professions, assessments of probability and risks are of critical importance—forecasting sales, calculating insurance needs and premiums, determining safety standards in engineering, and so on. In this section, we are not going to discuss the mathematics of probability. If you are interested, there are many textbooks and websites you can consult (including the companion website). Instead we shall focus on some of the main reasoning mistakes about probability. 17.4.1

Gambler's fallacy

The gambler's fallacy is the mistaken belief that the probability of an event might increase or decrease depending on the pattern of its recent occurrences, even though these events are independent of each other. The name comes from the

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fact that lots of people make this mistake when they gamble. For example, the probability of a fair coin landing on heads is V2. But suppose you toss the coin four times and it landed on heads each time. Someone who thinks it is more likely to be tails next time so that things will "balance out" is committing the gambler's fallacy. This is because the probability of a fair coin landing heads is just the same as the probability of landing tails, whatever the past results might have been. Similarly, it is also a fallacy to think that a series of four tails is more likely to be followed by yet another tail because the tail side is "hot." A good real-life example of the gambler's fallacy might be when people choose numbers for a lottery. Let's say the winning numbers of the last lottery are 2,4,18, 27, 29, 36. Most people would choose a different set of numbers when they play the lottery, thinking that their combination is more likely to win than the previous winning combination. But this is a fallacy, because if the lottery is a fair one, all combinations are equally likely, or better, equally unlikely! A very dangerous manifestation of the gambler's fallacy is the hot hand fallacy. This happens when a gambler wins a few times in a row, and he thinks he is on a lucky streak. As a result, he thinks he is more likely to win than lose if he continues to gamble. But this is a fallacy because the probability of him winning the next round is independent of his past record. It is a dangerous fallacy because very often these gamblers start to feel they are invincible and so they increase their wager and end up losing all their money. 17.4.2

Regression fallacy

Regression fallacy is a mistake of causal reasoning due to the failure to consider how things fluctuate randomly, typically around some average condition. Intense pain, exceptional sports performance, and high stock prices are likely to be followed by more subdued conditions eventually due to natural fluctuation. Failure to recognize this fact can lead to wrong conclusions about causation. For example, someone might suffer from back pain now and then but nothing seems to solve the problem completely. During a period of very intense pain, the patient decided to try alternative therapy like putting a magnetic patch on his back. He felt less pain afterward and concluded that the patch worked. But this could just be the result of regression. If he sought treatment when the pain was very intense, it is quite possible that the pain has already reached its peak and would lessen in any case as part of the natural cycle. Inferring that the patch was effective ignored a relevant alternative explanation. Similarly, sometimes we are lucky in the sense that things go very well, and other times we are unlucky and everything seems to go wrong. This is just an inevitable fact of life. But if we read too much into it, we might think we need to do something to improve our luck, and look for solutions where none is needed, such as using crystals to boost our karma. Of course, it is important to reflect on ourselves when things are not working well since it could be due to personal failings such as not working hard enough. What is needed is a careful and objective evaluation of the situation.

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17.4.3

Amazing coincidences

Here is a story about an amazing coincidence (Michell and Rickard, 1977): In 1975, a man was riding a moped in Bermuda and was killed by a taxi. A year later his brother was riding the same moped and died in the same way. In fact he was hit by the same taxi driver, and carrying the same passenger! There are many stories about similar coincidences.1 Some are quite creepy and makes you wonder whether there might be any hidden meaning to them. This is a normal reaction since human beings naturally seek patterns and explanations. But we should not ignore the fact that improbable things do happen simply as a matter of probability. Otherwise we might end up accepting rather implausible theories. Here are some examples: • It is claimed that some photos of the explosion of the World Trade Center Towers during the terrorist attack on September 11, 2001 seem to show the face of the devil in the smoke. But given the amount of video footage and photos that were taken, it is not surprising that some parts of the smoke might be seen to resemble something else. • The Bible Code is the idea that the Bible includes hidden messages about important world events and predictions about the future. To decode the messages, arrange the letters of the Hebrew Bible text in an array leaving out spaces and punctuation marks. Then start from a location in the text, and selects every nth letter from that location either forward or backward. You might then be able to find references to famous Jewish people, former U.S. President Bill Clinton, Hitler, and so on. However, the problem is that given a huge number of letters, it is not surprising that some random combination of these letters can produce meaningful words or even sentences. People have shown that the same can be done with Tolstoy's War and Peace and the novel Moby Dick. A useful reminder relevant to this topic is Littlewood's law, named after J. E. Littlewood (1885-1977), a Cambridge mathematician. According to this so-called law, miracles happen quite frequently, around once a month. Littlewood's argument starts with the definition of a miracle as an exceptional event with an extremely low probability of one in a million. But suppose a person is awake for eight hours a day, seven days a week, and experiencing about one event per second (watching a particular scene on TV or hearing a sound). Such a person will experience about one million events in 35 days, and so we expect this person to encounter a miracle about once a month! Of course, you might protest that a miracle must be some kind of meaningful event, or perhaps an event with an even lower probability. But whatever the details might be, Littlewood's point is that 1

Search for "amazing coincidences" on the web.

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seemingly miraculous events are bound to happen given lots of random events. This is a fact about statistics, even if it might be difficult (or disappointing) to believe otherwise. EXERCISES 17.1

Discuss and evaluate these claims and arguments related to statistics: a) The average man has about 3 sexual partners. The Playboy magazine interviewed 217 of its male reader and their average number of sexual partners is 2.9. b) It is bad reasoning for a cook to check the quality of a big pot of soup by tasting just a spoonful because the sample size is too small. c) Statistics indicate that if people like you take up smoking, they will increase their chance of getting lung cancer by 100%. Since you do smoke, you have a 100% chance of getting lung cancer. d) Married Korean men like to spend their holidays with their families. In a survey carried out last Sunday outside the Toys R Us store at the Nuzzon mall in Seoul, 76% of married men surveyed said that they prefer to spend their holidays with family members. e) I have counted about 34 students skipping Professor Awful's class, but only 6 for Professor Funny. So it is probably true that Professor Funny's class is more interesting. f ) According to a study presented by KO Management research at the World Economic Forum, 72% of respondents who rate their organization highly for actively promoting health and well-being also rate it highly for encouraging creativity and innovation. As we can see, if companies want to become more creative and innovative, they need to promote employee health and well-being. g) The store advertisement says that the average price of their video games is $9.1 have exactly $10 with me, so the majority of the games should be within my budget. h) A new drug for preventing heart attacks offers a 20% improvement compared with the standard one! It is twice as expensive, but it is worth it.

17.2

Are the sentences in each pair equivalent to each other? a) 68% teenagers voted. 32% teenagers did not vote. b) 30% strongly approve. 70% strongly disapprove. c) Unemployment is up 6%. Unemployment is at 6%. d) GDP growth is declining. GDP growth is weak.

17.3

Consider the following diagrams and see if they are misleading in any way. a) This chart shows the number of people surveyed who agree or disagree with building a new tunnel:

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4,123

agree

disagree

b) This chart shows a company's profits in 2010 and 2011. €31,000 €16,200

2010

2011

c) Failure rate in a class from 2000 to 2004.

2000 01 02 03 04 d) A chart showing the n u m b e r of households in a village participating in a recycling scheme in 2000 and 2010. 310 156

® 2000

^ 2010

e) Average length offish caught in a river. 70

2010

2011

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f) Number of pets kept by students in a school. ke ;

y

^=5

=5